Research ArticleOpen AccessGoogle Scholar indexed
Domination Number of Square of Cartesian Products of Cycles
Islamic Azad University, Nazarabad Branch
Islamic Azad University, Nazarabad Branch
- 1 Islamic Azad University, Nazarabad Branch
- 2 Islamic Azad University, Nazarabad Branch
Open Journal of Discrete Mathematics·Volume 05 (2015)·Pages 88–94·Published 12 August 2015·DOI10.4236/ojdm.2015.54008
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Abstract
A set is a dominating set of G if every vertex of is adjacent to at least one vertex of S . The cardinality of the smallest dominating set of G is called the domination number of G . The square G 2 of a graph G is obtained from G by adding new edges between every two vertices having distance 2 in G . In this paper we study the domination number of square of graphs, find a bound for domination number of square of Cartesian product of cycles, and find the exact value for some of them.
KeywordsDomination NumberSquare of a GraphCartesian Product
- West, D.B. (2001) Introduction to Graph Theory. 2nd Edition, Prentice-Hall, Upper Saddle River.
- Haynes, T., Hedetniemi, S. and Slater, P.J. (1997) Fundamentals of Domination in Graphs. M. dekker, Inc., New York.
- Ore, O. (1962) Theory of Graphs. American Mathematical Society Colloquium Publications, 38 (American Mathematical Society, Providence, RI).
- Cockayne, E.J., Ko, C.W. and Shepherd, F.B. (1985) Inequalities Concerning Dominating Sets in Graphs. Technical Report DM-370-IR, Department of Mathematics, University of Victoria.
- Walikar, H.B., Acharya, B.D. and Sampathkumar, E. (1979) Recent Developments in the Theory of Domination in Graphs. In MRI Lecture Notes in Math. Mehta Research Institute of Mathematics, Allahabad, Vol. 1.
- Vizing, V.G. (1963) The Cartesian Product of Graphs. Vycisl. Sistemy, 9, 30-43.