on the szeged index of non-commutative graph of general linear group

Let gg be a non-abelian group and let z(g) be the center of gg. associate with gg there is agraph γg as follows: take g∖z(g) as vertices ofγg and joint two distinct vertices xx and yy wheneveryx≠yx. γgγg is called the non-commuting graph of gg. 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 γpsl(2,q), where q≡0(mod 4)q≡0(mod 4). in this paper we will compute the szeged index forγpsl(2,q) where q≢0(mod 4).