3-Tuple domination number in complete grid graphs
J. Mehri, Mirkamal Mirnia, Seyed Mahmoud Sheikholeslami · International Mathematical Forum · 2006
In a graph G, a vertex dominates itself and its neighbors. A subset S ⊆ V (G) isak-tuple dominating set of G if each vertex of G is dominated by at least k vertices of S. Ak-tuple dominating set S of a graph G is perfect if each vertex of G is dominated by exactly k vertices in S. The k-tuple domination number γ×k(G) is the minimum cardinality among all k-tuple dominating sets of G. In this note we determine the 3-tuple domination number γ×3 for the complete grid graphs Pn × Pm for 2 ≤ n ≤ 4 and m ≥ 1. We also study the existence and construction of perfect 3-tuple dominating sets in this graphs.