A note on the k-tuple domination number of graphs - Cabrera Martinez, Abel (Ars mathematica contemporanea, 2022)
In a graph ?$G$?, a vertex dominates itself and its neighbours. A set ?$D \subseteq V(G)$? 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-dominacija; k-domination; k-kratna dominacija; k-tuple domination