Common neighborhood spectrum of commuting graphs of finite groups, By Reza Sharafdini

Research

Title	Common neighborhood spectrum of commuting graphs of finite groups
Type	Article
Keywords	commuting graph, spectrum, integral graph, finite group
Journal	Algebra and Discrete Mathematics
DOI	http://dx.doi.org/10.12958/adm1332
Researchers	Walaa Nabil Taha Fasfous (First researcher) , Reza Sharafdini (Second researcher) , Rajat Kanti Nath (Third researcher)

Abstract

The commuting graph of a finite non-abelian group \(G\) with center \(Z(G)\), denoted by \(\Gamma_c(G)\), is a simple undirected graph whose vertex set is \(G\setminus Z(G)\), and two distinct vertices \(x\) and \(y\) are adjacent if and only if \(xy = yx\). In this paper, we compute the common neighborhood spectrum of commuting graphs of several classes of finite non-abelian groups and conclude that these graphs are CN-integral.