On some properties of partial dominating sets

A subset of the vertex set of a graph is a dominating set of the graph if that subset and all the adjacent vertices of that subset form the whole of the vertex set. In case, if a subset and all the adjacent vertices of that subset form part of the whole set, say, for 0 < p < 1, ptimes of the whole vertex set, we say it is a partial domination. In this paper, we explore some of the properties of partial dominating sets with respect to particular values of p.