SPECTRAL PROPERTIES OF NC-GRAPHS

Let G be a non-abelian group and Z (G) be the center of G. The non-commuting graph (NC-graph) Gamma(G) of the group G is a graph with the vertex set G \ Z (G) and two distinct vertices x and y are adjacent whenever xy not equal yx. The aim of this paper is to prove that for given group G, G/Z(G) congruent to Z(p) x Z(p) if and only if Z (G) Gamma(G) is a regular (p - 1)-partite graph. Also we consider the isomorphism of the non-commuting graph with some special graphs.