Domination Number of Square of Cartesian Products of Cycles
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.
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.
Cite this paper
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.
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.
References
[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.
[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.