ON THE GROUPS WITH THE PARTICULARNON-COMMUTING GRAPHS

Let G be a non-abelian nite group. In this paper, we prove that ??(G) is K4-free, if and only if G ? A ? P, where A is an abelian group, P is a 2-group and G=Z(G) ? Z² ? Z². Also, we show that ??(G) is K¹;³-free if and only if G? S³; D8 or Q8.

Keywords:

Non-commuting graph , K4-free graph , K¹ , ³-free graph