A note on the k-tuple domination number of graphs

Abel Cabrera Martínez

Abstract


In a graph G, a vertex dominates itself and its neighbours. A set D ⊆ V(G) is said to be a k-tuple dominating set of G if D dominates every vertex of G at least k times. The minimum cardinality among all k-tuple dominating sets is the k-tuple domination number of G. In this note, we provide new bounds on this parameter. Some of these bounds generalize other ones that have been given for the case k = 2.


Keywords


k-domination, k-tuple domination

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DOI: https://doi.org/10.26493/1855-3974.2600.dcc

ISSN: 1855-3974

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