On the Aα-Eigenvalues of Signed Graphs

Germain Pastén, Óscar Rojo, Luis Medina

Type: Article

Publication Date: 2021-08-20

Citations: 2

DOI: https://doi.org/10.3390/math9161990

Abstract

For α∈[0,1], let Aα(Gσ)=αD(G)+(1−α)A(Gσ), where G is a simple undirected graph, D(G) is the diagonal matrix of its vertex degrees and A(Gσ) is the adjacency matrix of the signed graph Gσ whose underlying graph is G. In this paper, basic properties of Aα(Gσ) are obtained, its positive semidefiniteness is studied and some bounds on its eigenvalues are derived—in particular, lower and upper bounds on its largest eigenvalue are obtained.

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