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 $qnotequiv 0 (mod ~~ 4)$.