The Clique Number Of The Non-commuting Graph Of Groups Of Order P~5

Assume G is a group. The non-commuting graph of G is defined as the graph whose vertex set is G\Z(G) and two vertices are joint if and only if they do not commute. In this paper, we study the clique number ω(G) of the non-commuting graph of groups of order p5. When p=2 or 3, we give ω(G) for all 118 groups; If p≥5, then there are 61 type of groups. Except 6 type of groups, we give ω(G) for each group.