Let  denote the minimum cardinality among all maximal independent sets of G containing v, i.e.,  is the minimum cardinality among all independent dominating sets of G containing v. Then  is called the independent dom-saturation number of G. In this paper, we elaborate a study of independent dom-saturation number of a graph G. We also introduce the concept of is-bondage number. An is-bondage number of G is defined to be the minimum number of edges whose removal increases the value of is. In this paper, we obtain basic results of is-bondage number.

domination, independent domination, independence, independent dom-saturation number.