$k$-Isolate domination number of simple graphs

G. Rajasekar, A. Jeslet Kani Bala
2019 Malaya Journal of Matematik  
In this paper we introduce k -isolate dominating set and minimal k -isolate dominating set and it is defined as follows: A dominating set S of a graph G is said to be a k -isolate dominating set if S has at least k -isolated vertices. The k -isolate dominating set S is said to be a minimal k -isolate dominating set if any proper subset of S is not an isolate dominating set. The minimum and the maximum cardinality of a minimal k -isolate dominating set of G are called k -isolate domination
more » ... te domination number denoted by γ ki (G) and the upper k -isolate domination number by Γ ki (G) respectively. Also k-isolate domination number for some simple graphs such as path, cycle and wheel graph have been found.
doi:10.26637/mjm0s01/0027 fatcat:xuovbnnajbaevbtnflqtulkswi