Some algebraic properties of a class of integral graphs determined by their spectrum

2019/05/25 by Jia‐Bao Liu, Liu, Jia-Bao, S. Morteza Mirafzal +3
Chemistry · Mathematics · #05C31 #05C50 #Combinatorics (math.CO) #FOS: Mathematics #Finite Group Theory Research #Graph theory and applications #Synthesis and Properties of Aromatic Compounds

paper · pdf · doi:10.48550/arxiv.1905.10525

openalex publication_date 2019/05/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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=Cay(ℤ_n, S), where n=p^m, (p is a prime integer, m∈ℕ) and S=\a∈ℤ_n | (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 K_v \bigtriangledownΓ are determined by their spectrum.

Related

• Integral Cayley graphs and groups
• Integral Cayley graphs over a finite symmetric algebra
• Integral Cayley graphs of symmetric groups on transpositions
• On groups all of whose undirected Cayley graphs of bounded valency are\n integral
• Integral cographs and applications