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Extended results on two domination number and chromatic number of a graph

Keywords: Two Domination Number , Chromatic Number

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Abstract:

A subset S of V is called a dominating set in G if every vertex in V-S is adjacent to at least one vertex in S. A Dominating set is said to be two dominating set if every vertex in V-S 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 2n-5 and 2n-6. In this paper, we characterize all graphs whose sum of two domination number and chromatic number is 2n-7.

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