A note on integral non-commuting graphs

The non-commuting graph Γ(G) of group G is a graph with the vertex set G − Z(G) and two distinct vertices x and y are adjacent whenever xy = yx. In this paper, we compute the spectrum of non-commuting graphs of some wellknown groups. Further, if G is a non-abelian finite group and its non-commuting graph Γ(G) is k−regular, then we prove k = 2sq where q is an odd prime.