Total Dominator Color Class Total Dominating Sets in Necklace Graph, Hurdle Graph and F-Tree Graph
Keywords:
Chromatic number, Domination number, Color class dominating set, Dominator color class dominating set, Total dominator color class total domination number.Abstract
Let be a finite, undirected and connected graph with minimum degree at least one. 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(G). 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 by . Here we obtain for Necklace graph, Hurdle graph and F-tree graph.
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