On Laplacian energy of non-commuting graphs of finite groups

Subject Areas : Combinatorics, Graph theory

P.  Dutta ¹ (Department of Mathematical Sciences, Tezpur University, Napaam-784028, Sonitpur, Assam, India)
R. K.  Nath ² (Department of Mathematical Sciences, Tezpur University, Napaam-784028, Sonitpur, Assam, India)

Received: 2017-12-13 Accepted : 2018-04-30 Published : 2018-06-01

Keywords: Non-commuting graph, L-spectrum, Laplacian energy, finite group,

Abstract :

‎Let $G$ be a finite non-abelian group with center $Z(G)$‎. ‎The non-commuting graph of $G$ is a simple undirected graph whose vertex set is $G\setminus Z(G)$ and two vertices $x$ and $y$ are adjacent if and only if $xy \ne yx$‎. ‎In this paper‎, we compute Laplacian energy of the non-commuting graphs of some classes of finite non-abelian groups‎..

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