Domination Number of Square of Cartesian Products of Cycles


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 G2 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.

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Alishahi, M. and Shalmaee, S. (2015) Domination Number of Square of Cartesian Products of Cycles. Open Journal of Discrete Mathematics, 5, 88-94. doi: 10.4236/ojdm.2015.54008.

Conflicts of Interest

The authors declare no conflicts of interest.


[1] West, D.B. (2001) Introduction to Graph Theory. 2nd Edition, Prentice-Hall, Upper Saddle River.
[2] Haynes, T., Hedetniemi, S. and Slater, P.J. (1997) Fundamentals of Domination in Graphs. M. dekker, Inc., New York.
[3] Ore, O. (1962) Theory of Graphs. American Mathematical Society Colloquium Publications, 38 (American Mathematical Society, Providence, RI).
[4] 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.
[5] 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.
[6] Vizing, V.G. (1963) The Cartesian Product of Graphs. Vycisl. Sistemy, 9, 30-43.

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