# ON THE SZEGED INDEX OF NON-COMMUTATIVE GRAPH OF GENERAL LINEAR GROUP

Authors

Arak University

Abstract

Let $G$ be a non-abelian group and let $Z(G)$ be the center of $G$. Associate with $G$ there is a
graph $\Gamma_G$ as follows: Take $G\setminus Z(G)$ as vertices of
$\Gamma_G$ and joint two distinct vertices $x$ and $y$ whenever
$yx\neq yx$. $\Gamma_G$ is called the non-commuting graph of $G$.
In recent years many interesting works have been done in non-commutative graph of groups.
Computing the clique number, chromatic number, Szeged index and  Wiener index play important role in graph theory. In particular, the clique
number of non-commuting graph of some the general linear groups has been determined.

\nt Recently, Wiener and Szeged indices
have been computed for $\Gamma_{PSL(2,q)}$, where $q\equiv 0 (mod ~~4)$. In this paper we will compute the Szeged index for
$\Gamma_{PSL(2,q)}$, where $q\not\equiv 0 (mod ~~ 4)$.

Keywords

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