Global dominator coloring of graphs
M. Rajeswari, I. Sahul Hamid · Discussiones Mathematicae Graph Theory · 2018
Let S V . A vertex v V is a dominator of S if v dominates every vertex in S and v is said to be an anti-dominator of S if v dominates none of the vertices of S. Let C = (V 1 , V 2 , . . . , V k ) be a coloring of G and let v V (G). A color class V i is called a dom-color class or an anti domcolor class of the vertex v according as v is a dominator of V i or an antidominator of V i . The coloring C is called a global dominator coloring of G if every vertex of G has a dom-color class and an anti dom-color class in C. The minimum number of colors required for a global dominator coloring of G is called the global dominator chromatic number and is denoted by gd (G). This paper initiates a study on this notion of global dominator coloring.