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 G\setminus Z(G) as vertices of\Gamma_G and joint two distinct vertices x and y wheneveryx\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 indiceshave been computed for \Gamma_{PSL(۲,q)}, where q\equiv ۰ (mod~~۴). In this paper we will compute the Szeged index for\Gamma_{PSL(۲,q)}, where q\not\equiv ۰ (mod ~~ ۴).

Keywords:

Non-commuting grapg , general Linear group , Szeged index