# ON DOMINATION NUMBER OF CARTESIAN PRODUCT OF EVEN CYCLES

## Abstract

Let Î³(G) denote the domination number of the graph G and let Î³(GH) denote the domination number of the Cartesian product of the graphs and . Here in this note; let denote the cycle with three vertices and similarly, let denote the cycle with n vertices. The domination number of the Cartesian product of two even cycles and is characterized here, wherem< , with such that G H C3 Cn Cm Cn n m â‰¥ 4 m n mn Î³(C C )= 4 if and only if 2 divides mn 4 , that is, iff mn 2 | 4## References

V. G. Vizing, Vychisl, Sistemy 90, 63 (1963)

V. G. Vizing, Uspehi Mat. Nauk 23 (1986)

M. El-Zahar and C. M. Pareek, Ars Combin.

(1991) 223.

R.J. Faudree and R. H. Schelp, Congr.

Numer. 79 (1990) 29.

W. T. Tutte, Graph Theory, Cambridge

University Press (2001).

M. S. Jacobson and L. F. Kinch, J. Graph

Theory 10 (1986) 97.

J.A. Bondy and U.S.R. Murty, Graph Theory,

Springer (2010).

J.A. Gallian, Electronic J. Combinatorics,

DS6 (Jan.3, 2007) 1.

S. Klavzar and N. Seifter, Discrete Applied

Mathematics 59 (1995) 97.

D. GonÃ§alves, A. Pinlou, M. Rao and S.

ThomassÃ©, The Domination Number of

Grids, 2011arXiv1102.5206G

A. Klobucar, Mathematical Communications

(2004) 35.

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## How to Cite

*The Nucleus*, vol. 48, no. 4, pp. 269–272, Dec. 2011.