Some Algebraic Properties of a Class of Integral Graphs Determined by Their Spectrum

Jia-Bao Liu, S. Morteza Mirafzal, Ali Zafari and Ghulam Mustafa

Journal of Mathematics, 2021, vol. 2021, 1-5

Abstract: Let Γ=V,E be a graph. If all the eigenvalues of the adjacency matrix of the graph Γ are integers, then we say that Γ is an integral graph. A graph Γ is determined by its spectrum if every graph cospectral to it is in fact isomorphic to it. In this paper, we investigate some algebraic properties of the Cayley graph Γ=Cayℤn,S, where n=pm (p is a prime integer and m∈ℕ) and S=a∈ℤn|a,n=1. First, we show that Γ is an integral graph. Also, we determine the automorphism group of Γ. Moreover, we show that Γ and Kv▽Γ are determined by their spectrum.

Date: 2021
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jjmath:6632206

DOI: 10.1155/2021/6632206

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