Domination Number of Square of Cartesian Products of Cycles

Morteza Alishahi; Sakineh Hoseini Shalmaee

doi:10.4236/ojdm.2015.54008

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Open Journal of Discrete Mathematics > Vol.5 No.4, October 2015

Domination Number of Square of Cartesian Products of Cycles ()

Morteza Alishahi^*, Sakineh Hoseini Shalmaee

Islamic Azad University, Nazarabad Branch.

DOI: 10.4236/ojdm.2015.54008 PDF HTML XML 3,748 Downloads 4,598 Views Citations

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 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.

Keywords

Domination Number, Square of a Graph, Cartesian Product

Share and Cite:

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.

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