Commuting Graphs on Dihedral Group

Let ? be a non-abelian group and ? ? ?. The commuting graph C(?, ?), has ? as its vertex set with two distinct elements of ? joined by an edge when they commute in ?. In this paper we discuss certain properties of commuting graphs constructured on the dihedral group D with respect to some specific subsets. More specifically we obtain the chromatic number and clique number of these commuting graphs. 2n