Global dominating sets in minimum coloring

Abstract

In this paper, we introduce the concept of global dominating-χ-coloring of a graph and the corresponding parameter namely global dominating-χ-color number. Let G be a graph. Among all χ-colorings of G, a coloring with the maximum number of color classes that are global dominating sets in G is called a global dominating-χ-coloring of G. The number of color classes that are global dominating sets in a global dominating-χ-coloring of G is defined to be the global dominating-χ-color number of G, denoted by gd χ(G).