Total Domination Subdivision Number in Strong Product Graph

P. Jeyanthi^1, , G. Hemalatha² and B. Davvaz³

¹Department of Mathematics, Govindammal Aditanar College for Women, Tiruchendur, Tamil Nadu, India

²Department of mathematics, Shri Andal Alagar College of Engineering, Mamandur, Kancheepuram, Tamil Nadu, India

³Department of Mathematics, Yazd University, Yazd, Iran

Cite this paper

P. Jeyanthi, G. Hemalatha and B. Davvaz. Total Domination Subdivision Number in Strong Product Graph. American Journal of Applied Mathematics and Statistics. 2014; 2(4):216-219. doi: 10.12691/AJAMS-2-4-7

Abstract

A set D of vertices in a graph G(V,E) is called a total dominating set if every vertex v∈V is adjacent to an element of D. The domination subdivision number of a graph G is the minimum number of edges that must be subdivided in order to increase the domination number of a graph. In this paper, we determine the total domination number for strong product graph and establish bounds on the total domination subdivision number for strong product graph.

Keywords

total dominating set, strong product graph, total domination number

Copyright

This work is licensed under a Creative Commons Attribution 4.0 International License. To view a copy of this license, visit http://creativecommons.org/licenses/by/4.0/

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