Relation Between Dominating and Total Dominating Color Transversal number of Graphs
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Keywords:
Total Dominating Color Transversal number, Dominating Color Transversal number, $\chi$- Partition of a graphAbstract
Total Dominating Color Transversal Set is the combination of three very well known concepts of graph theory, viz., Total Dominating Set, Transversal and Proper Coloring of vertices of a graph. It is defined as a Total Dominating Set which is also Transversal of Some $\chi$-Partition of vertices of G. Here $\chi$ is the Chromatic number of the graph G. Total Dominating Color Transversal number of a graph is the cardinality of a Total Dominating Color Transversal Set which has minimum cardinality among all such sets that the graph admits. Analogously, R. L. J. Manoharan defined Dominating Color Transversal number of a graph in [2]. In this paper we investigate some relations between these two numbers. We give sufficient examples to justify our results.
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