Fu‐Gang Yin

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All published works (39)

Symmetric Cayley graphs on non-abelian simple groups of valency 7

2025-05-01

Xing Zhang , Yan‐Quan Feng , Fu‐Gang Yin +1 more

Normal edge-transitive Cayley graphs on non-abelian simple groups

2025-04-02

Xing Zhang , Yan‐Quan Feng , Fu‐Gang Yin +1 more

Application of maximal subgroups of exceptional groups in s-arc-transitivity of vertex-primitive digraphs (I)

2025-02-17

Fu‐Gang Yin , Lei Chen

The investigation of maximal subgroups of simple groups of Lie type is intimately related to the study of primitive actions. With the recent publication of Craven's paper giving the complete … The investigation of maximal subgroups of simple groups of Lie type is intimately related to the study of primitive actions. With the recent publication of Craven's paper giving the complete list of the maximal subgroups of $F_{4}(q)$, $E_{6}(q)$ and ${}^{2}E_{6}(q)$, we are able to thoroughly analyse the primitive action of an exceptional group on an $s$-arc-transitive digraph and partially answer the following question posed by Giudici and Xia: Is there an upper bound on $s$ for finite vertex-primitive $s$-arc-transitive digraphs that are not directed cycles? Giudici and Xia reduced this question to the case where the automorphism group of the digraph is an almost simple group. Subsequently, it was proved that $s\leq 2$ when the simple group is a projective special linear group, projective symplectic group or an alternating group, and $s\leq 1$ when the simple group is a Suzuki group, a small Ree group, or one of the 22 sporadic groups. In this work, we proved that $s\leq 2$ when the simple group is $ {}^3D_4(q)$, $G_2(q)$, ${}^2F_4(q)$, $F_4(q)$, $E_6(q)$ or ${}^2E_6(q)$.

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The classification of two-distance transitive dihedrants

2025-01-01

Junjie Huang , Yan‐Quan Feng , Jin‐Xin Zhou +1 more

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Symmetric Cayley graphs on non-abelian simple groups of valency 7

2024-09-27

Xing Zhang , Yan‐Quan Feng , Fu‐Gang Yin +1 more

Let $\Gamma$ be a connected $7$-valent symmetric Cayley graph on a finite non-abelian simple group $G$. If $\Gamma$ is not normal, Li {\em et al.} [On 7-valent symmetric Cayley graphs … Let $\Gamma$ be a connected $7$-valent symmetric Cayley graph on a finite non-abelian simple group $G$. If $\Gamma$ is not normal, Li {\em et al.} [On 7-valent symmetric Cayley graphs of finite simple groups, J. Algebraic Combin. 56 (2022) 1097-1118] characterised the group pairs $(\mathrm{soc}(\mathrm{Aut}(\Gamma)/K),GK/K)$, where $K$ is a maximal intransitive normal subgroup of $\mathrm{Aut}(\Gamma)$. In this paper, we improve this result by proving that if $\Gamma$ is not normal, then $\mathrm{Aut}(\Gamma)$ contains an arc-transitive non-abelian simple normal subgroup $T$ such that $G<T$ and $(T,G)=(\mathrm{A}_{n},\mathrm{A}_{n-1})$ with $n=7$, $3\cdot 7$, $3^2\cdot 7$, $2^2\cdot 3\cdot 7$, $2^3\cdot3\cdot7$, $2^3\cdot3^2\cdot5\cdot7$, $2^4\cdot3^2\cdot5\cdot7$, $2^6\cdot3\cdot7$, $2^7\cdot3\cdot7$, $2^6\cdot3^2\cdot7$, $2^6\cdot3^4\cdot5^2\cdot7$, $2^8\cdot3^4\cdot5^2\cdot7$, $2^7\cdot3^4\cdot5^2\cdot7$, $2^{10}\cdot3^2\cdot7$, $2^{24}\cdot3^2\cdot7$. Furthermore, $\mathrm{soc}(\mathrm{Aut}(\Gamma)/R)=(T\times R)/R$, where $R$ is the largest solvable normal subgroup of $\mathrm{Aut}(\Gamma)$.

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On isomorphisms of $m$-Cayley digraphs

2024-09-01

Xing Zhang , Yuan-Quan Feng , Fu‐Gang Yin +1 more

The isomorphism problem for digraphs is a fundamental problem in graph theory. This problem for Cayley digraphs has been extensively investigated over the last half a century. In this paper, … The isomorphism problem for digraphs is a fundamental problem in graph theory. This problem for Cayley digraphs has been extensively investigated over the last half a century. In this paper, we consider this problem for $m$-Cayley digraphs which are generalization of Cayley digraphs. Let $m$ be a positive integer. A digraph admitting a group $G$ of automorphisms acting semiregularly on the vertices with exactly $m$ orbits is called an $m$-Cayley digraph of $G$. In particular, $1$-Cayley digraph is just the Cayley digraph. We first characterize the normalizer of $G$ in the full automorphism group of an $m$-Cayley digraph of a finite group $G$. This generalizes a similar result for Cayley digraph achieved by Godsil in 1981. Then we use this to study the isomorphisms of $m$-Cayley digraphs. The CI-property of a Cayley digraph (CI stands for `Cayley isomorphism') and the DCI-groups (whose Cayley digraphs are all CI-digraphs) are two key topics in the study of isomorphisms of Cayley digraphs. We generalize these concepts into $m$-Cayley digraphs by defining $m$CI- and $m$PCI-digraphs, and correspondingly, $m$DCI- and $m$PDCI-groups. Analogues to Babai's criterion for CI-digraphs are given for $m$CI- and $m$PCI-digraphs, respectively. With these we then classify finite $m$DCI-groups for each $m\geq 2$, and finite $m$PDCI-groups for each $m\geq 4$. Similar results are also obtained for $m$-Cayley graphs. Note that 1DCI-groups are just DCI-groups, and the classification of finite DCI-groups is a long-standing open problem that has been worked on a lot.

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A complete classification of edge-primitive graphs of valency 6

2024-08-12

Cixuan Wu , Fu‐Gang Yin

Block-Transitive Steiner 3-Designs on 2-Transitive Groups

2024-07-31

Weijun Liu , Ting Lan , Fu‐Gang Yin

In 2005, Huber proved that the flag-transitive group of automorphisms for a Steiner [Formula: see text]-design must act [Formula: see text]-transitively on the point set. He also classified flag-transitive Steiner … In 2005, Huber proved that the flag-transitive group of automorphisms for a Steiner [Formula: see text]-design must act [Formula: see text]-transitively on the point set. He also classified flag-transitive Steiner [Formula: see text]-designs. It should be noted that while flag-transitive designs are block-transitive, the converse is not always true. Furthermore, all known block-transitive Steiner [Formula: see text]-designs have [Formula: see text]-transitive automorphism groups. In this study, we consider [Formula: see text]-block-transitive Steiner [Formula: see text]-designs [Formula: see text] with [Formula: see text] acting [Formula: see text]-transitively on the point set, and prove that if [Formula: see text] is not [Formula: see text]-flag-transitive, then either [Formula: see text] is a [Formula: see text]-[Formula: see text]-design with the Suzuki group as its automorphism group, or [Formula: see text] is a subgroup of [Formula: see text] and the size of the block is an odd integer.

On m-partite oriented semiregular representations of finite groups generated by two elements

2024-04-24

Jia‐Li Du , Young Soo Kwon , Fu‐Gang Yin

Block-transitive 3-(v, k, 1) designs on exceptional groups of Lie type

2024-04-06

Ting Lan , Weijun Liu , Fu‐Gang Yin

On 2-distance primitive graphs of prime valency

2024-03-26

Junjie Huang , Yan‐Quan Feng , Young Soo Kwon +2 more

The classification of two-distance transitive dihedrants

2024-03-01

Junjie Huang , Yan‐Quan Feng , Jin‐Xin Zhou +1 more

A vertex transitive graph $\Gamma$ is said to be $2$-distance transitive if for each vertex $u$, the group of automorphisms of $\Gamma$ fixing the vertex $u$ acts transitively on the … A vertex transitive graph $\Gamma$ is said to be $2$-distance transitive if for each vertex $u$, the group of automorphisms of $\Gamma$ fixing the vertex $u$ acts transitively on the set of vertices at distance $1$ and $2$ from $u$, while $\Gamma$ is said to be $2$-arc transitive if its automorphism group is transitive on the set of $2$-arcs. Then $2$-arc transitive graphs are $2$-distance transitive. The classification of $2$-arc transitive Cayley graphs on dihedral groups was given by Du, Malni\v{c} and Maru\v{s}i\v{c} in [Classification of 2-arc-transitive dihedrants, J. Combin. Theory Ser. B 98 (2008), 1349--1372]. In this paper, it is shown that a connected 2-distance transitive Cayley graph on the dihedral group of order $2n$ is either $2$-arc transitive, or isomorphic to the complete multipartite graph $K_{m[b]}$ for some $m\geq3$ and $b\geq2$ with $mb=2n$.

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Cubic Graphs Admitting Vertex-Transitive Almost Simple Groups

2023-10-28

Jia‐Li Du , Fu‐Gang Yin , Menglin Ding

Two-geodesic transitive graphs of order p with n ≤ 3

2023-09-18

Junjie Huang , Yan‐Quan Feng , Jin‐Xin Zhou +1 more

Block-transitive 3-(v, k, 1) designs associated with alternating groups

2023-05-15

Ting Lan , Weijun Liu , Fu‐Gang Yin

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The smallest vertex-primitive 2-arc-transitive digraph

2023-03-21

Fu‐Gang Yin , Yan‐Quan Feng , Binzhou Xia

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Block-transitive $3$-$(v,k,1)$ designs on exceptional groups of Lie type

2023-01-01

Ting Lan , Weijun Liu , Fu‐Gang Yin

Let $\mathcal{D}$ be a non-trivial $G$-block-transitive $3$-$(v,k,1)$ design, where $T\leq G \leq \mathrm{Aut}(T)$ for some finite non-abelian simple group $T$. It is proved that if $T$ is a simple exceptional … Let $\mathcal{D}$ be a non-trivial $G$-block-transitive $3$-$(v,k,1)$ design, where $T\leq G \leq \mathrm{Aut}(T)$ for some finite non-abelian simple group $T$. It is proved that if $T$ is a simple exceptional group of Lie type, then $T$ is either the Suzuki group ${}^2B_2(q)$ or $G_2(q)$. Furthermore, if $T={}^2B_2(q)$ then the design $\mathcal{D}$ has parameters $v=q^2+1$ and $k=q+1$, and so $\mathcal{D}$ is an inverse plane of order $q$; and if $T=G_2(q)$ then the point stabilizer in $T$ is either $\mathrm{SL}_3(q).2$ or $\mathrm{SU}_3(q).2$, and the parameter $k$ satisfies very restricted conditions.

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Quasiprimitive groups with a biregular dihedral subgroup,and arc-transitive bidihedrants

2023-01-01

Jiangmin Pan , Fu‐Gang Yin , Jin‐Xin Zhou

A semiregular permutation group on a set $\Ome$ is called {\em bi-regular} if it has two orbits. A classification is given of quasiprimitive permutation groups with a biregular dihedral subgroup. … A semiregular permutation group on a set $\Ome$ is called {\em bi-regular} if it has two orbits. A classification is given of quasiprimitive permutation groups with a biregular dihedral subgroup. This is then used to characterize the family of arc-transitive graphs whose automorphism groups containing a bi-regular dihedral subgroup. We first show that every such graph is a normal $r$-cover of an arc-transitive graph whose automorphism group is either quasiprimitive or bi-quasiprimitive on its vertices, and then classify all such quasiprimitive or bi-quasiprimitive arc-transitive graphs.

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Prime-valent symmetric graphs with a quasi-semiregular automorphism

2022-12-14

Fu‐Gang Yin , Yan‐Quan Feng , Jin‐Xin Zhou +1 more

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2-Arc-transitive Cayley graphs on alternating groups

2022-08-04

Jiangmin Pan , Binzhou Xia , Fu‐Gang Yin

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Two-geodesic transitive graphs of order $p^n$ with $n\leq3$

2022-01-01

Huang Junjie , Yan‐Quan Feng , Jin‐Xin Zhou +1 more

A vertex triple $(u,v,w)$ of a graph is called a $2$-geodesic if $v$ is adjacent to both $u$ and $w$ and $u$ is not adjacent to $w$. A graph is … A vertex triple $(u,v,w)$ of a graph is called a $2$-geodesic if $v$ is adjacent to both $u$ and $w$ and $u$ is not adjacent to $w$. A graph is said to be $2$-geodesic transitive if its automorphism group is transitive on the set of $2$-geodesics. In this paper, a complete classification of $2$-geodesic transitive graphs of order $p^n$ is given for each prime $p$ and $n\leq 3$. It turns out that all such graphs consist of three small graphs: the complete bipartite graph $K_{4,4}$ of order $8$, the Schl\"{a}fli graph of order $27$ and its complement, and fourteen infinite families: the cycles $C_p, C_{p^2}$ and $C_{p^3}$, the complete graphs $K_p, K_{p^2}$ and $K_{p^3}$, the complete multipartite graphs $K_{p[p]}$, $K_{p[p^2]}$ and $K_{p^2[p]}$, the Hamming graph $H(2,p)$ and its complement, the Hamming graph $H(3,p)$, and two infinite families of normal Cayley graphs on extraspecial group of order $p^3$ and exponent $p$.

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Block-transitive $3$-$(v,k,1)$ designs associated with alternating groups

2022-01-01

Ting Lan , Weijun Liu , Fu‐Gang Yin

Let $\mathcal{D}$ be a nontrivial $3$-$(v,k,1)$ design admitting a block-transitive group $G$ of automorphisms. A recent work of Gan and the second author asserts that $G$ is either affine or … Let $\mathcal{D}$ be a nontrivial $3$-$(v,k,1)$ design admitting a block-transitive group $G$ of automorphisms. A recent work of Gan and the second author asserts that $G$ is either affine or almost simple. In this paper, it is proved that if $G$ is almost simple with socle an alternating group, then $\mathcal{D}$ is the unique $3$-$(10,4,1)$ design, and $G=\mathrm{PGL}(2,9)$, $\mathrm{M}_{10}$ or $\mathrm{Aut}(\mathrm{A}_6 )=\mathrm{S}_6:\mathrm{Z}_2$, and $G$ is flag-transitive.

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The smallest vertex-primitive $2$-arc-transitive digraph

2022-01-01

Fu‐Gang Yin , Yan‐Quan Feng , Binzhou Xia

In 2017, Giudici, Li and the third author constructed the first known family of vertex-primitive $2$-arc-transitive digraphs of valency at least $2$. The smallest digraph in this family admits $\mathrm{PSL}_3(49)$ … In 2017, Giudici, Li and the third author constructed the first known family of vertex-primitive $2$-arc-transitive digraphs of valency at least $2$. The smallest digraph in this family admits $\mathrm{PSL}_3(49)$ acting $2$-arc-transitively with vertex-stabilizer $\mathrm{A}_6$ and hence has $30758154560$ vertices. In this paper, we prove that this digraph is the vertex-primitive $2$-arc-transitive digraph of valency at least $2$ with fewest vertices.

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The symmetry property of (n,k)‐arrangement graph

2021-06-09

Fu‐Gang Yin , Yan‐Quan Feng , Jin‐Xin Zhou +1 more

Abstract The ‐ arrangement graph with , is the graph with vertex set the ordered ‐tuples of distinct elements in and with two ‐tuples adjacent if they differ in exactly … Abstract The ‐ arrangement graph with , is the graph with vertex set the ordered ‐tuples of distinct elements in and with two ‐tuples adjacent if they differ in exactly one of their coordinates. The ‐arrangement graph was proposed by Day and Tripathi in 1992, and is a widely studied interconnection network topology. The Johnson graph with , is the graph with vertex set the ‐element subsets of , and with two ‐element subsets adjacent if their intersection has elements. In 1989, Brouwer, Cohen and Neumaier determined the automorphism group of , and in 2015, Dobson and Malnič proved that a is Cayley graph if and only if , or with being a prime‐power. In this article we prove that , and as a byproduct, is a normal cover of . Furthermore, is a Cayley graph if and only if , , , , , , , , , , , or , where is a prime‐power. Note that the graph is called the ‐ star graph , and its automorphism group can be deduced from a general result given by Feng in 2006. In 1998, Chiang and Chen proved that is a Cayley graph on the alternating group , and in 2011, Zhou determined the automorphism group of .

On edge-transitive bi-Frobenius-metacirculants

2021-04-23

Jiangmin Pan , Fu‐Gang Yin

Finite edge-transitive bi-circulants

2021-04-18

Jiangmin Pan , Fu‐Gang Yin

Symmetric graphs of valency 4 having a quasi-semiregular automorphism

2021-02-02

Fu‐Gang Yin , Yan‐Quan Feng

2-Arc-transitive Cayley graphs on alternating groups

2021-01-01

Jiangmin Pan , Binzhou Xia , Fu‐Gang Yin

An interesting fact is that most of the known connected $2$-arc-transitive nonnormal Cayley graphs of small valency on finite simple groups are $(\mathrm{A}_{n+1},2)$-arc-transitive Cayley graphs on $\mathrm{A}_n$. This motivates the … An interesting fact is that most of the known connected $2$-arc-transitive nonnormal Cayley graphs of small valency on finite simple groups are $(\mathrm{A}_{n+1},2)$-arc-transitive Cayley graphs on $\mathrm{A}_n$. This motivates the study of $2$-arc-transitive Cayley graphs on $\mathrm{A}_n$ for arbitrary valency. In this paper, we characterize the automorphism groups of such graphs. In particular, we show that for a non-complete $(G,2)$-arc-transitive Cayley graph on $\mathrm{A}_n$ with $G$ almost simple, the socle of $G$ is either $\mathrm{A}_{n+1}$ or $\mathrm{A}_{n+2}$. We also construct the first infinite family of $(\mathrm{A}_{n+2},2)$-arc-transitive Cayley graphs on $\mathrm{A}_n$.

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Prime-valent Symmetric graphs with a quasi-semiregular automorphism

2021-01-01

Fu‐Gang Yin , Yan‐Quan Feng , Jin‐Xin Zhou +1 more

An automorphism of a graph is called quasi-semiregular if it fixes a unique vertex of the graph and its remaining cycles have the same length. This kind of symmetry of … An automorphism of a graph is called quasi-semiregular if it fixes a unique vertex of the graph and its remaining cycles have the same length. This kind of symmetry of graphs was first investigated by Kutnar, Malni\v{c}, Mart\'{i}nez and Maru\v{s}i\v{c} in 2013, as a generalization of the well-known semiregular automorphism of a graph. Symmetric graphs of valency three or four, admitting a quasi-semiregular automorphism, have been classified in recent two papers. Let $p\geq 5$ be a prime and $\Gamma$ a connected symmetric graph of valency $p$ admitting a quasi-semiregular automorphism. In this paper, we first prove that either $\Gamma$ is a connected Cayley graph $\rm{Cay}(M,S)$ such that $M$ is a $2$-group admitting a fixed-point-free automorphism of order $p$ with $S$ as an orbit of involutions, or $\Gamma$ is a normal $N$-cover of a $T$-arc-transitive graph of valency $p$ admitting a quasi-semiregular automorphism, where $T$ is a non-abelian simple group and $N$ is a nilpotent group. Then in case $p=5$, we give a complete classification of such graphs $\Gamma$ such that either $\rm{Aut}(\Gamma)$ has a solvable arc-transitive subgroup or $\Gamma$ is $T$-arc-transitive with $T$ a non-abelian simple group. We also construct the first infinite family of symmetric graphs that have a quasi-semiregular automorphism and an insolvable full automorphism group.

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On generalized truncations of complete graphs

2020-11-20

Xue Wang , Fu‐Gang Yin , Jin‐Xin Zhou

For a k-regular graph Γ and a graph Υ of order k, a generalized truncation of Γ by Υ is constructed by replacing each vertex of Γ with a copy … For a k-regular graph Γ and a graph Υ of order k, a generalized truncation of Γ by Υ is constructed by replacing each vertex of Γ with a copy of Υ. E. Eiben, R. Jajcay and P. Šparl introduced a method for constructing vertex-transitive generalized truncations. For convenience, we call a graph obtained by using Eiben et al.’s method a special generalized truncation. In their paper, Eiben et al. proposed a problem to classify special generalized truncations of a complete graph Kn by a cycle of length n − 1. In this paper, we completely solve this problem by demonstrating that with the exception of n = 6, every special generalized truncation of a complete graph Kn by a cycle of length n − 1 is a Cayley graph of AGL(1, n) where n is a prime power. Moreover, the full automorphism groups of all these graphs and the isomorphisms among them are determined.

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Arc-transitive Cayley graphs on nonabelian simple groups with prime valency

2020-07-31

Fu‐Gang Yin , Yan‐Quan Feng , Jin‐Xin Zhou +1 more

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Arc-transitive Cayley graphs on nonabelian simple groups with prime valency

2020-01-01

Fu‐Gang Yin , Yan‐Quan Feng , Jin‐Xin Zhou +1 more

In 2011, Fang et al. in (J. Combin. Theory A 118 (2011) 1039-1051) posed the following problem: Classify non-normal locally primitive Cayley graphs of finite simple groups of valency $d$, … In 2011, Fang et al. in (J. Combin. Theory A 118 (2011) 1039-1051) posed the following problem: Classify non-normal locally primitive Cayley graphs of finite simple groups of valency $d$, where either $d\leq 20$ or $d$ is a prime number. The only case for which the complete solution of this problem is known is of $d=3$. Except this, a lot of efforts have been made to attack this problem by considering the following problem: Characterize finite nonabelian simple groups which admit non-normal locally primitive Cayley graphs of certain valency $d\geq4$. Even for this problem, it was only solved for the cases when either $d\leq 5$ or $d=7$ and the vertex stabilizer is solvable. In this paper, we make crucial progress towards the above problems by completely solving the second problem for the case when $d\geq 11$ is a prime and the vertex stabilizer is solvable.

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Vertex-primitive s-arc-transitive digraphs of alternating and symmetric groups

2019-10-23

Jiangmin Pan , Cixuan Wu , Fu‐Gang Yin

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Arc-transitive Cayley graphs on non-abelian simple groups with soluble vertex stabilizers and valency seven

2018-11-29

Jiangmin Pan , Fu‐Gang Yin , Bo Ling

Edge-primitive Cayley graphs on abelian groups and dihedral groups

2018-09-18

Jiangmin Pan , Cixuan Wu , Fu‐Gang Yin

Finite edge-primitive graphs of prime valency

2018-06-17

Jiangmin Pan , Cixuan Wu , Fu‐Gang Yin

Vertex-primitive s-arc-transitive digraphs of alternating and symmetric groups

2018-01-01

Jiangmin Pan , Cixuan Wu , Fu‐Gang Yin

A fascinating problem on digraphs is the existence problem of the finiteupper bound on s for all vertex-primitive s-arc-transitive digraphs except directed cycles (which is known to be reduced to … A fascinating problem on digraphs is the existence problem of the finiteupper bound on s for all vertex-primitive s-arc-transitive digraphs except directed cycles (which is known to be reduced to the almost simple groups case). In this paper,we prove that s 2 for all G-vertex-primitive s-arc-transitive digraphs with G an (insoluble) alternating or symmetric group, which makes an important progress towards a solution of the problem. The proofs involves some methods that may be used to investigate other almost simple groups cases.

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Symmetric graphs of order four times a prime power and valency seven

2017-05-25

Jiangmin Pan , Fu‐Gang Yin

In this paper, we study symmetric graphs of valency seven and order [Formula: see text] with [Formula: see text] a prime and [Formula: see text] an arbitrary positive integer. It … In this paper, we study symmetric graphs of valency seven and order [Formula: see text] with [Formula: see text] a prime and [Formula: see text] an arbitrary positive integer. It is proved that no such graph exists for any prime [Formula: see text], thus reducing the study to the case [Formula: see text]. The result is then used to determine all such graphs of order [Formula: see text], and such graphs of order [Formula: see text] with ‘[Formula: see text]’ can be inductively investigated similarly.

Arc-transitive Cayley graphs on non-ableian simple groups with soluble vertex stabilizers and valency seven

2017-01-01

Jiangmin Pan , Fu‐Gang Yin , Bo Ling

In this paper, we study arc-transitive Cayley graphs on non-abelian simple groups with soluble stabilizers and valency seven. Let $\Ga$ be such a Cayley graph on a non-abelian simple group … In this paper, we study arc-transitive Cayley graphs on non-abelian simple groups with soluble stabilizers and valency seven. Let $\Ga$ be such a Cayley graph on a non-abelian simple group $T$. It is proved that either $\Ga$ is a normal Cayley graph or $\Ga$ is $S$-arc-transitive, with $(S,T)=(\A_n,\A_{n-1})$ and $n=7,21,63$ or $84$; and, for each of these four values of $n$, there really exists arc-transitive $7$-valent non-normal Cayley graphs on $\A_{n-1}$ and specific examples are constructed.

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Common Coauthors

Coauthor	Papers Together
Yan‐Quan Feng	16
Jin‐Xin Zhou	14
Jiangmin Pan	12
Binzhou Xia	4
Junjie Huang	4
Weijun Liu	4
Xing Zhang	3
Cixuan Wu	3
Bo Ling	2
Ting Lan	2
Ting Lan	2
Hong Wang	2
Jia‐Li Du	2
Cixuan Wu	2
Young Soo Kwon	2
A-Hui Jia	2
Yuhong Guo	1
Huang Junjie	1
Xue Wang	1
Xing Zhang	1
Ting Lan	1
Shan-Shan Chen	1
Menglin Ding	1
Yuan-Quan Feng	1
Shanshan Chen	1
Lei Chen	1
Weijun Liu	1

Commonly Cited References

The Magma Algebra System I: The User Language

1997-09-01

Wieb Bosma , John Cannon , Catherine Playoust

On the full automorphism group of a graph

1981-09-01

Chris Godsil

An O'Nan-Scott Theorem for Finite Quasiprimitive Permutation Groups and an Application to 2-Arc Transitive Graphs

1993-04-01

Cheryl E. Praeger

A permutation group is said to be quasiprimitive if each of its nontrivial normal subgroups is transitive. A structure theorem for finite quasiprimitive permutation groups is proved, along the lines … A permutation group is said to be quasiprimitive if each of its nontrivial normal subgroups is transitive. A structure theorem for finite quasiprimitive permutation groups is proved, along the lines of the O'Nan-Scott Theorem for finite primitive permutation groups. It is shown that every finite, non-bipartite, 2-arc transitive graph is a cover of a quasiprimitive 2-arc transitive graph. The structure theorem for quasiprimitive groups is used to investigate the structure of quasiprimitive 2-arc transitive graphs, and a new construction is given for a family of such graphs.

Finite 2-arc-transitive abelian Cayley graphs

2006-12-31

Cai Heng Li , Jiangmin Pan

5-Arc transitive cubic Cayley graphs on finite simple groups

2006-03-01

Shang Jin Xu , Xin Fang , Jie Wang +1 more

Tetravalent 2-arc-transitive Cayley graphs on non-abelian simple groups

2019-05-06

Jia‐Li Du , Yan‐Quan Feng

Let G be a finite non-abelian simple group and let Γ be a connected tetravalent 2-arc-transitive G-regular graph. In 2004, Fang, Li, and Xu proved that either G is normal … Let G be a finite non-abelian simple group and let Γ be a connected tetravalent 2-arc-transitive G-regular graph. In 2004, Fang, Li, and Xu proved that either G is normal in the full automorphism group Aut(Γ) of Γ, or G is one of up to 22 exceptional candidates. In this paper, the number of exceptions is reduced to 7, and for each one, it is shown that Aut(Γ) has a normal arc-transitive non-abelian simple subgroup T such that G≤T and the pair (G, T) is explicitly given. Furthermore, there exists a G-regular (T,2)-arc-transitive graph for each of the 7 pairs (G, T).

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On the Automorphism Groups of Cayley Graphs of Finite Simple Groups

2002-12-01

Xin Fang , Cheryl E. Praeger , Jie Wang

Let G be a finite nonabelian simple group and let Γ be a connected undirected Cayley graph for G. The possible structures for the full automorphism group AutΓ are specified. … Let G be a finite nonabelian simple group and let Γ be a connected undirected Cayley graph for G. The possible structures for the full automorphism group AutΓ are specified. Then, for certain finite simple groups G, a sufficient condition is given under which G is a normal subgroup of AutΓ. Finally, as an application of these results, several new half-transitive graphs are constructed. Some of these involve the sporadic simple groups G = J1, J4, Ly and BM, while others fall into two infinite families and involve the Ree simple groups and alternating groups. The two infinite families contain examples of half-transitive graphs of arbitrarily large valency.

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Permutation Groups

1996-01-01

John D. Dixon , Brian Mortimer

On edge-transitive Cayley graphs of valency four

2004-02-10

Xin Fang , Cai Heng Li , Ming Xu

Arc-transitive Cayley graphs on non-abelian simple groups with soluble vertex stabilizers and valency seven

2018-11-29

Jiangmin Pan , Fu‐Gang Yin , Bo Ling

On cubic s-arc transitive Cayley graphs of finite simple groups

2004-04-18

Shang Jin Xu , Xin Fang , Jie Wang +1 more

Finite Permutation Groups and Finite Simple Groups

1981-01-01

Peter J‎. Cameron

A classification of the maximal subgroups of the finite alternating and symmetric groups

1987-12-01

Martin W. Liebeck , Cheryl E. Praeger , Jan Saxl

Pentavalent symmetric graphs admitting vertex-transitive non-abelian simple groups

2017-04-04

Jia‐Li Du , Yan‐Quan Feng , Jin‐Xin Zhou

Finite Simple Groups

1982-01-01

Daniel Gorenstein

Vertex-transitive graphs: Symmetric graphs of prime valency

1984-03-01

Peter Lorimer

Abstract Let G be a group acting symmetrically on a graph Σ, let G 1 be a subgroup of G minimal among those that act symmetrically on Σ, and let … Abstract Let G be a group acting symmetrically on a graph Σ, let G 1 be a subgroup of G minimal among those that act symmetrically on Σ, and let G 2 be a subgroup of G 1 maximal among those normal subgroups of G 1 which contain no member except 1 which fixes a vertex of Σ. The most precise result of this paper is that if Σ has prime valency p , then either Σ is a bipartite graph or G 2 acts regularly on Σ or G 1 | G 2 is a simple group which acts symmetrically on a graph of valency p which can be constructed from Σ and does not have more vertices than Σ. The results on vertex‐transitive groups necessary to establish results like this are also included.

Factorizations of Almost Simple Groups with a Solvable Factor, and Cayley Graphs of Solvable Groups

2022-07-26

Cai Heng Li , Binzhou Xia

A characterization is given for the factorizations of almost simple groups with a solvable factor. It turns out that there are only several infinite families of these nontrivial factorizations, and … A characterization is given for the factorizations of almost simple groups with a solvable factor. It turns out that there are only several infinite families of these nontrivial factorizations, and an almost simple group with such a factorization cannot have socle exceptional Lie type or orthogonal of minus type. The characterization is then applied to study <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="s"> <mml:semantics> <mml:mi>s</mml:mi> <mml:annotation encoding="application/x-tex">s</mml:annotation> </mml:semantics> </mml:math> </inline-formula>-arc-transitive Cayley graphs of solvable groups, leading to a striking corollary that, except for cycles, a non-bipartite connected <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="3"> <mml:semantics> <mml:mn>3</mml:mn> <mml:annotation encoding="application/x-tex">3</mml:annotation> </mml:semantics> </mml:math> </inline-formula>-arc-transitive Cayley graph of a finite solvable group is necessarily a normal cover of the Petersen graph or the Hoffman-Singleton graph.

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On locally primitive Cayley graphs of finite simple groups

2010-11-09

Xingui Fang , Xuesong Ma , Jie Wang

Isomorphisms of finite Cayley graphs

1997-08-01

Cai Heng Li

An abstract is not available for this content so a preview has been provided. As you have access to this content, a full PDF is available via the ‘Save PDF’ … An abstract is not available for this content so a preview has been provided. As you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

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Automorphism groups and isomorphisms of Cayley digraphs

1998-03-01

Mingyao Xu

On weakly symmetric graphs of order twice a prime

1987-04-01

Ying Cheng , James Oxley

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Arc-transitive Cayley graphs on nonabelian simple groups with prime valency

2020-07-31

Fu‐Gang Yin , Yan‐Quan Feng , Jin‐Xin Zhou +1 more

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Distance-Regular Graphs

1989-01-01

Andries E. Brouwer , Arjeh M. Cohen , Arnold Neumaier

Finite edge-transitive Cayley graphs and rotary Cayley maps

2006-05-09

Cai Heng Li

This paper aims to develop a theory for studying Cayley graphs, especially for those with a high degree of symmetry. The theory consists of analysing several types of basic Cayley … This paper aims to develop a theory for studying Cayley graphs, especially for those with a high degree of symmetry. The theory consists of analysing several types of basic Cayley graphs (normal, bi-normal, and core-free), and analysing several operations of Cayley graphs (core quotient, normal quotient, and imprimitive quotient). It provides methods for constructing and characterising various combinatorial objects, such as half-transitive graphs, (orientable and non-orientable) regular Cayley maps, vertex-transitive non-Cayley graphs, and permutation groups containing certain regular subgroups. In particular, a characterisation is given of locally primitive holomorph Cayley graphs, and a classification is given of rotary Cayley maps of simple groups. Also a complete classification is given of primitive permutation groups that contain a regular dihedral subgroup.

s-Arc-transitive graphs and normal subgroups

2014-09-17

Cai Heng Li , Ákos Seress , Shu Jiao Song

Atlas of Finite Groups--Maximal Subgroups and Ordinary Characters for Simple Groups.

1987-01-01

R. Steinberg , J. H. Conway , Robert T. Curtis +3 more

This atlas covers groups from the families of the classification of finite simple groups. Recently updated incorporating corrections This atlas covers groups from the families of the classification of finite simple groups. Recently updated incorporating corrections

Locally primitive Cayley graphs of dihedral groups

2013-08-20

Jiangmin Pan

A graph Γ is called locally-primitive if the vertex stabilizer (AutΓ)α is primitive on the neighbor set of α for each vertex α. In this paper, we classify locally-primitive Cayley … A graph Γ is called locally-primitive if the vertex stabilizer (AutΓ)α is primitive on the neighbor set of α for each vertex α. In this paper, we classify locally-primitive Cayley graphs of dihedral groups, while 2-arc-transitive Cayley graphs of dihedral groups have been classified by a series of papers in the literature.

(G,s)-Transitive Graphs of Valency 7

2016-06-20

Songtao Guo , Yantao Li , Xiaohui Hua

Let X be a finite simple undirected graph and G an automorphism group of X. If G is transitive on s-arcs but not on (s+1)-arcs then X is called (G,s)-transitive. … Let X be a finite simple undirected graph and G an automorphism group of X. If G is transitive on s-arcs but not on (s+1)-arcs then X is called (G,s)-transitive. Let X be a connected (G,s)-transitive graph of a prime valency p, and G v the vertex stabilizer of a vertex v ∈ V(X) in G. For the case p=3, the exact structure of G v has been determined by Djoković and Miller in [Regular groups of automorphisms of cubic graphs, J. Combin. Theory (Ser. B) 29 (1980) 195 – 230]. For the case p=5, all the possibilities of G v have been given by Guo and Feng in [A note on pentavalent s-transitive graphs, Discrete Math.312 (2012) 2214 – 2216]. In this paper, we deal with the case p=7 and determine the exact structure of the vertex stabilizer G v .

A note on solvable vertex stabilizers of s-transitive graphs of prime valency

2015-09-01

Songtao Guo , Hailong Hou , Yong Xu

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Semiregular automorphisms of vertex-transitive cubic graphs

2005-06-24

Peter J‎. Cameron , J. Sheehan , Pablo Spiga

Classification of 2-arc-transitive dihedrants

2008-04-02

Shaofei Du , Aleksander Malnič , Dragan Marušič

The finite primitive groups with soluble stabilizers, and the edge-primitive <i>s</i> -arc transitive graphs

2011-02-28

Cai Heng Li , Hua Zhang

Motivated by the study of several problems in algebraic graph theory, we study finite primitive permutation groups whose point stabilizers are soluble. Such primitive permutation groups are divided into three … Motivated by the study of several problems in algebraic graph theory, we study finite primitive permutation groups whose point stabilizers are soluble. Such primitive permutation groups are divided into three types: affine, almost simple and product action, and the product action type can be reduced to the almost simple type. This paper gives an explicit list of the soluble maximal subgroups of almost simple groups. The classification is then applied to classify edge-primitive s-arc transitive graphs with s ⩾ 4, solving a problem proposed by Richard M. Weiss (1999).

Arc-transitive graphs of square-free order and small valency

2016-07-01

Cai Heng Li , Zai Ping Lu , Wang Gai-xia

A note on pentavalent <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si1.gif" display="inline" overflow="scroll"><mml:mi>s</mml:mi></mml:math>-transitive graphs

2012-05-16

Songtao Guo , Yan‐Quan Feng

Arc-transitive graphs of valency 8 have a semiregular automorphism

2014-04-14

Gabriel Verret

One version of the polycirculant conjecture states that every vertex-transitive graph has a non-identity semiregular automorphism that is, a non-identity automorphism whose cycles all have the same length. We give … One version of the polycirculant conjecture states that every vertex-transitive graph has a non-identity semiregular automorphism that is, a non-identity automorphism whose cycles all have the same length. We give a proof of the conjecture in the arc-transitive case for graphs of valency 8, which was the smallest open valency.

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Locally <i>s</i>‐distance transitive graphs

2011-02-01

Alice Devillers , Michael Giudici , Cai Heng Li +1 more

Abstract We give a unified approach to analyzing, for each positive integer s , a class of finite connected graphs that contains all the distance transitive graphs as well as … Abstract We give a unified approach to analyzing, for each positive integer s , a class of finite connected graphs that contains all the distance transitive graphs as well as the locally s ‐arc transitive graphs of diameter at least s . A graph is in the class if it is connected and if, for each vertex v , the subgroup of automorphisms fixing v acts transitively on the set of vertices at distance i from v , for each i from 1 to s . We prove that this class is closed under forming normal quotients. Several graphs in the class are designated as degenerate, and a nondegenerate graph in the class is called basic if all its nontrivial normal quotients are degenerate. We prove that, for s ≥2, a nondegenerate, nonbasic graph in the class is either a complete multipartite graph or a normal cover of a basic graph. We prove further that, apart from the complete bipartite graphs, each basic graph admits a faithful quasiprimitive action on each of its (1 or 2) vertex‐orbits or a biquasiprimitive action. These results invite detailed additional analysis of the basic graphs using the theory of quasiprimitive permutation groups. © 2011 Wiley Periodicals, Inc. J Graph Theory 69:176‐197, 2012

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Quasi m-Cayley circulants

2012-06-15

Ademir Hujdurović

A graph Γ is called a quasi m-Cayley graph on a group G if there exists a vertex ∞ ∈ V (Γ ) and a subgroup G of the vertex … A graph Γ is called a quasi m-Cayley graph on a group G if there exists a vertex ∞ ∈ V (Γ ) and a subgroup G of the vertex stabilizer Aut(Γ ) ∞ of the vertex ∞ in the full automorphism group Aut(Γ ) of Γ , such that G acts semiregularly on V (Γ ) ∖ {∞} with m orbits. If the vertex ∞ is adjacent to only one orbit of G on V (Γ ) ∖ {∞} , then Γ is called a strongly quasi m -Cayley graph on G . In this paper complete classifications of quasi 2 -Cayley, quasi 3 -Cayley and strongly quasi 4 -Cayley connected circulants are given.

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The finite edge-primitive pentavalent graphs

2012-11-29

Songtao Guo , Yan‐Quan Feng , Cai Heng Li

A family of cubical graphs

1947-10-01

W. T. Tutte

We begin with some definitions. A cubical graph is a simplicial 1-complex in which each 0-simplex is incident with just three 1-simplexes. We begin with some definitions. A cubical graph is a simplicial 1-complex in which each 0-simplex is incident with just three 1-simplexes.