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arXiv · 2310.20230

On the eigenvalues and Seidel eigenvalues of chain graphs

Zhuang Xiong·Yaoping Hou
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Abstract

In this paper we consider the eigenvalues and the Seidel eigenvalues of a chain graph. An$\dbar$elić, da Fonseca, Simić, 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}.

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Zhuang Xiong, Yaoping Hou. 2023-10-31. On the eigenvalues and Seidel eigenvalues of chain graphs. https://arxiv.org/abs/2310.20230

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