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 *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.

A set is a dominating set of

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.

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.