Dominator color class dominating sets in Grid graphs

Abstract

Let  be a graph. Let  be a proper coloring of .  is called dominator color class dominating set if each vertex  in  is dominated by a color class and each    is dominated by  a vertex  in . The dominator color class domination number is the minimum cardinality taken over all dominator color class dominating sets in  is denoted by . In this paper, we obtain  for Grid graph.