A note on the k -domination number of a graph

Y. Caro and Y. Roditty

International Journal of Mathematics and Mathematical Sciences, 1990, vol. 13, 1-2

Abstract:

The k -domination number of a graph G = G ( V , E ) , γ k ( G ) , is the least cardinality of a set X ⊂ V such that any vertex in V X is adjacent to at least k vertices of X .

Extending a result of Cockayne, Gamble and Shepherd [4], we prove that if δ ( G ) ≥ n + 1 n k − 1 , n ≥ 1 , k ≥ 1 then, γ k ( G ) ≤ n p n + 1 , where p is the order of G .

Date: 1990
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jijmms:796320

DOI: 10.1155/S016117129000031X

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