Let G be a non-abelian group and let Z(G) be the center of G. Associate with G there is a graph G as follows: Take G\Z(G) as vertices of G 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. Recently, Wiener and Szeged indices have been computed for G , where q = 0(mod 4). In this
