The graphical complexity of direct products of permutation groups

Mariusz Grech

Type: Article

Publication Date: 2010-12-16

Citations: 5

DOI: https://doi.org/10.1002/jgt.20504

Abstract

In this article, we improve known results, and, with one exceptional case, prove that when k≥3, the direct product of the automorphism groups of graphs whose edges are colored using k colors, is itself the automorphism group of a graph whose edges are colored using k colors. We have handled the case k = 2 in an earlier article. We prove similar results for directed edge-colored graphs. © 2010 Wiley Periodicals, Inc. J Graph Theory 66:303-318, 2011

Locations

Journal of Graph Theory - View - PDF

Similar Works

Action	Title	Year	Authors
+	Graphical complexity of products of permutation groups	2007	Mariusz Grech Artur Jeż Andrzej Kisielewicz
+ PDF Chat	Decompositions of the automorphism groups of edge-colored graphs into the direct product of permutation groups	2021	Mariusz Grech
+	Decompositions of the authomorphism groups of edge-colored graphs into the direct product of permutation groups	2019	Mariusz Grech
+	Complexity of homomorphisms to direct products of graphs	2002	Judit Büki Csaba Szabó
+	Direct products of automorphism groups of graphs	2009	Mariusz Grech
+	Direct product of automorphism groups of colored graphs	2004	Mariusz Grech Andrzej Kisielewicz
+	Direct product of automorphism groups of digraphs	2017	Wilfried Imrich
+ PDF Chat	Direct product of automorphism groups of digraphs	2019	Mariusz Grech Wilfried Imrich Anna Dorota Krystek Łukasz Jan Wojakowski
+	The coloring numbers of the direct product of two hypergraphs	1974	C. Berge Miklós Simonovits
+	Cayley graphs and direct-product graphs	1993	Arnold L. Rosenberg
+	Graphs and Direct Sum Matrices	1961	Z. Netter
+	The homomorphism and coloring of the direct product of signed graphs	2024	Chao Wen Qiang Sun Hongyan Cai Huanhuan Guan Chao Zhang
+	On the relational complexity of a finite permutation group	2019	Nick Gill
+ PDF Chat	On the relational complexity of a finite permutation group	2015	Gregory Cherlin
+	Representations of graphs by means of products and their complexity	1981	Jaroslav Nešetřil
+	Circular Chromatic Numbers of the Direct Product of Graphs	2005	Lingling Huang
+	Graphical Cyclic Permutation Groups	2012	Mariusz Grech
+	Graphical Cyclic Permutation Groups	2012	Mariusz Grech
+	Graphical cyclic permutation groups	2014	Mariusz Grech
+	Permutation Groups: A Complexity Overview	2003	Ákos Seress

Works That Cite This (5)

Action	Title	Year	Authors
+	Graphical cyclic permutation groups	2014	Mariusz Grech
+ PDF Chat	Direct product of automorphism groups of digraphs	2019	Mariusz Grech Wilfried Imrich Anna Dorota Krystek Łukasz Jan Wojakowski
+	None	2009	Stanislav Jendrol’ J. Miškuf Roman Soták Erika Škrabuľáková
+ PDF Chat	Decompositions of the automorphism groups of edge-colored graphs into the direct product of permutation groups	2021	Mariusz Grech
+ PDF Chat	Cyclic Permutation Groups that are Automorphism Groups of Graphs	2019	Mariusz Grech Andrzej Kisielewicz

Works Cited by This (18)

Action	Title	Year	Authors
+	On graphical regular representations of Cn × Q	1972	Mark E. Watkins
+	Direct product of automorphism groups of colored graphs	2004	Mariusz Grech Andrzej Kisielewicz
+	On the non-existence of graphs with transitive generalized dicyclic groups	1968	Lewis A. Nowitz
+	Graphical complexity of products of permutation groups	2007	Mariusz Grech Artur Jeż Andrzej Kisielewicz
+	Graphical regular representations of alternating, symmetric, and miscellaneous small groups	1974	Mark E. Watkins
+ PDF Chat	One‐factorizations of complete graphs with vertex‐regular automorphism groups	2001	Arrigo Bonisoli D. Labbate
+	None	2009	Meng Wei Shengjia Li Yubao Guo Gaokui Xu
+	Direct product and uniqueness of automorphism groups of graphs	1999	Wojciech Peisert
+	Homogeneous factorisations of graphs and digraphs	2004	Michael Giudici Cai Heng Li Primož Potočnik Cheryl E. Praeger
+	All Self-Complementary Symmetric Graphs	2001	Wojciech Peisert