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 ec- centric 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.
