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Section A

Bounds for the 2-domination number of toroidal grid graphs

Pages 584-588 | Received 14 May 2006, Accepted 10 Sep 2007, Published online: 24 Mar 2009
 

Abstract

A k-dominating set for a graph G(V, E) is a set of vertices DV such that every vertex vV\ D is adjacent to at least k vertices in D. The k-domination number of G, denoted by γ k (G), is the cardinality of a smallest k-dominating set of G. Here we establish lower and upper bounds of γ k (C m ×C n ) for k=2. In some cases, these bounds agree so that the exact 2-domination number is obtained.

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