Dominating-x-Color Number of Harary Graph

T. Ramachandran, A. Naseer Ahmed

Abstract: Let G = (V, E) be a graph. A graph G is k-colorable if it has a proper k-coloring. The chromatic number (G) is the least k such that G is k- colorable. In this paper, we examine the relation between the domination number, chromatic number and dominating -color number of Harary graph Hk, n. And we answer a question posed in [1] by showing that if q = 0, then (H_ (2r, n)) = p if not p + 1 such that n = (r + 1) s + t and n = ps + q with r t 0, s > q 0.

Keywords: Proper coloring, Chromatic number, Maximal independent set, Domination number, Dominating--color number