On the eigenvalues and Seidel eigenvalues of chain graphs
Combinatorics
2023-11-01 v1
Abstract
In this paper we consider the eigenvalues and the Seidel eigenvalues of a chain graph. Aneli\'{c}, da Fonseca, Simi\'{c}, and Du \cite{andelic2020tridiagonal} conjectured that there do not exist non-isomorphic cospectral chain graphs with respect to the adjacency spectrum. Here we disprove this conjecture. Furthermore, by considering the relation between the Seidel matrix and the adjacency matrix of a graph, we solve two problems on the number of distinct Seidel eigenvalues of a chain graph, which was posed by Mandal, Mehatari, and Das \cite{mandal2022spectrum}.
Cite
@article{arxiv.2310.20230,
title = {On the eigenvalues and Seidel eigenvalues of chain graphs},
author = {Zhuang Xiong and Yaoping Hou},
journal= {arXiv preprint arXiv:2310.20230},
year = {2023}
}
Comments
13 pages, 2 figures