On the Szeged and Eccentric connectivity indices of non-commutative graph of finite groups

Let G be a non-abelian group. The non-commuting graph ΓG of G is defined as the graph whose vertex set is the non-central elements of G and two vertices are joined if and only if they do not commute. In this paper we study some properties of ΓG and introduce n- regular AC-groups. Also we then obtain a formula for Szeged index of ΓG in terms of n, |Z(G)| and |G| . Moreover, we determine eccentric connectivity index of ΓG for every non-abelian finite group G in terms of the number of conjugacy classes k(G) and the size of the group G.