On domination number of Cartesian product of directed paths

Juan Liu (), Xindong Zhang and Jixiang Meng ()
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Juan Liu: Xinjiang University
Xindong Zhang: Xinjiang Normal University
Jixiang Meng: Xinjiang University

Journal of Combinatorial Optimization, 2011, vol. 22, issue 4, No 13, 662 pages

Abstract: Abstract Let γ(G) denote the domination number of a digraph G and let P m □P n denote the Cartesian product of P m and P n , the directed paths of length m and n. In this paper, we give a lower and upper bound for γ(P m □P n ). Furthermore, we obtain a necessary and sufficient condition for P m □P n to have efficient dominating set, and determine the exact values: γ(P 2□P n )=n, $\gamma(P_{3}\square P_{n})=n+\lceil\frac{n}{4}\rceil$ , $\gamma(P_{4}\square P_{n})=n+\lceil\frac{2n}{3}\rceil$ , γ(P 5□P n )=2n+1 and $\gamma(P_{6}\square P_{n})=2n+\lceil\frac{n+2}{3}\rceil$ .

Keywords: Cartesian product; Directed path; Domination number (search for similar items in EconPapers)
Date: 2011
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Citations: View citations in EconPapers (2)

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DOI: 10.1007/s10878-010-9314-x

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