On graphs with equal domination and 2-domination numbers

Let G be a simple graph, and let p be a positive integer. A subset image is a p-dominating set of the graph G, if every vertex image is adjacent to at least p vertices in D. The p-domination number image is the minimum cardinality among the p-dominating sets of G. Note that the 1-domination number image is the usual domination number image. This definition immediately leads to the inequality image. In this paper we present some sufficient as well as some necessary conditions for graphs G with the property that image. In particular, we characterize all cactus graphs H with image.