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 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.
A dominating set S which uniquely identify all vertices of the set V (G) − S is a locating dominating set. This paper presents the procedure for finding the location domination number of Corona product of graphs. And location domination number of graph of forms
In this paper Location-2-Domination set and their properties are being studied. A subset V S ⊆ is Location-2-Dominating set of G if S is 2-Dominating set of G and for any two vertices P W × , n m C S × P n ⋈P m , C n ⋈P m , C n ⋈C m have been found.
Locating dominating set is the subset of the vertex set which dominate and uniquely identify all vertices of the set . In this paper we formulated the apt method for finding the location domination number of sum of graphs based on the nature of the graphs and .
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