2023/10/31 by Zhuang Xiong, Yaoping Hou, Xiong, Zhuang +1
Chemistry · Computer Science · Mathematics · #Combinatorics (math.CO) #FOS: Mathematics #Graph theory and applications #Matrix Theory and Algorithms #Molecular spectroscopy and chirality
paper · pdf · doi:10.48550/arxiv.2310.20230
openalex publication_date 2023/10/31 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper we consider the eigenvalues and the Seidel eigenvalues of a chain graph. An\dbarelić, da Fonseca, Simić, and Du \citeandelic2020tridiagonal 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 \citemandal2022spectrum.