Arab Journal of Mathematical Sciences (Jul 2016)

Isolate domination in graphs

  • I. Sahul Hamid,
  • S. Balamurugan

DOI
https://doi.org/10.1016/j.ajmsc.2015.10.001
Journal volume & issue
Vol. 22, no. 2
pp. 232 – 241

Abstract

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A set D of vertices of a graph G is called a dominating set of G if every vertex in V(G)−D is adjacent to a vertex in D. A dominating set S such that the subgraph 〈S〉 induced by S has at least one isolated vertex is called an isolate dominating set. An isolate dominating set none of whose proper subset is an isolate dominating set is a minimal isolate dominating set. The minimum and maximum cardinality of a minimal isolate dominating set are called the isolate domination number γ0 and the upper isolate domination number Γ0 respectively. In this paper we initiate a study on these parameters.

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