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 a graph ΓG as follows: Take G∖Z(G) as vertices of ΓG and joint two distinct vertices x and y whenever yx≠yx. ΓG 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 ΓPSL(2,q), where q≡0(mod 4). In this paper we will compute the Szeged index for ΓPSL(2,q), where q≢0(mod 4) .