
Extended results on two domination number and chromatic number of a graphKeywords: Two Domination Number , Chromatic Number Abstract: A subset S of V is called a dominating set in G if every vertex in VS is adjacent to at least one vertex in S. A Dominating set is said to be two dominating set if every vertex in VS is adjacent to atleast two vertices in S. The minimum cardinality taken over all, the minimal two dominating set is called two domination number and is denoted by γ2 (G). The minimum number of colors required to colour all the vertices such that adjacent vertices do not receive the same colour is the chromatic number χ (G). In [6], it was proved that sum of two domination number and chromatic number is equals to 2n5 and 2n6. In this paper, we characterize all graphs whose sum of two domination number and chromatic number is 2n7.
