On the eigenvalues and Seidel eigenvalues of chain graphs
Abstract
In this paper we consider the eigenvalues and the Seidel eigenvalues of a chain graph. An\'c, da Fonseca, Simi\'c, and Du 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 mandal2022spectrum.
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