Total Dominator Color Class Total Dominating Sets In Star Relaed Graphs

Abstract

Let G =  be a finite, undirected and connected graph. A proper coloring  of G is said to be a total dominator color class total dominating set of G if each vertex properly dominates a color class in and each color class in  is properly dominated by a vertex in V. A total dominator color class total dominating set D of G is a minimal total dominator color class total dominating set if no proper subset of D is a total dominator color class total dominating set of G. The total dominator color class total domination number is the minimum cardinality taken over all minimal total dominator color class total dominating sets in G and is denoted byHere we obtain total dominator color class total domination number of modular star graph and kalami modular star graph.