Results on majority dom-chromatic sets of a graph

Abstract

A majority dominating set S ⊆ V (G) is said to be majority dominating chromatic set if S satisfies the condition χ(hSi) = χ(G). The majority dom-chromatic number γMχ(G) is the minimum cardinality of majority dominating chromatic set. In this article we investigated some inequalities on Majority dominating chromatic sets of a connected and disconnected graph G. Also characterization theorems and some results on majority dom-chromatic number γMχ(G) for a vertex color critical graph and biparte graph are determined. we established the relationship between three parameters namely χ(G), γM(G) and γMχ(G) for some graphs.