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

Let $G$ be a non-abelian group and let $Z(G)$ be the center of $G$. Associate with $G$ there is agraph $Gamma_G$ as follows: Take $Gsetminus Z(G)$ as vertices of$Gamma_G$ and joint two distinct vertices $x$ and $y$ whenever$yxneq yx$. $Gamma_G$ 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 indiceshave been computed for $Gamma_{PSL(2,q)}$, where $qequiv 0 (mod~~4)$. In this paper we will compute the Szeged index for$Gamma_{PSL(2,q)}$, where $qnotequiv 0 (mod ~~ 4)$.