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E.J. Cockayne, R.M. Dawes and S.T. Hedetniemi, Total dominations in graphs, Networks, 10 (1980), 211-219.

has been cited by the following article:

Article

Total Domination Subdivision Number in Strong Product Graph

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


American Journal of Applied Mathematics and Statistics. 2014, Vol. 2 No. 4, 216-219
DOI: 10.12691/ajams-2-4-7
Copyright © 2014 Science and Education Publishing

Cite this paper:
P. Jeyanthi, G. Hemalatha, 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.

Correspondence to: P.  Jeyanthi, Department of Mathematics, Govindammal Aditanar College for Women, Tiruchendur, Tamil Nadu, India. Email: jeyajeyanthi@rediffmail.com

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.

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