Discussiones Mathematicae Graph Theory 27(1) (2007) 175-178
doi: 10.7151/dmgt.1353

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TOTAL DOMINATION OF CARTESIAN PRODUCTS OF GRAPHS

Xinmin Hou

Department of Mathematics
University of Science and Technology of China
Hefei, Anhui, 230026, China
e-mail: xmhou@ustc.edu.cn

Abstract

Let γt(G) and γpr(G) denote the total domination and the paired domination numbers of graph G, respectively, and let G□H denote the Cartesian product of graphs G and H. In this paper, we show that γt(G)γt(H) ≤ 5γt(G□H), which improves the known result γt(G)γt(H) ≤ 6γt(G□H) given by Henning and Rall.

Keywords: total domination number, Cartesian product, Vizing's conjecture.

2000 Mathematics Subject Classification: 05C69.

References

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[5] V.G. Vizing, Some unsolved problems in graph theory, Usp. Mat. Nauk 23 (1968), no. 6(144) 117-134.

Received 7 March 2006
Revised 25 October 2006