On the $n-$dominating graph of specific graphs

Abstract

Let G = (V, E) be a graph. A set S ⊆ V (G) is a dominating set, if every vertex in V (G)\S is adjacent to at least one vertex in S. The k-dominating graph of G, D k (G), is defined to be the graph whose vertices correspond to the dominating sets of G that have cardinality at most k. Two vertices in D k (G) are adjacent if and only if the corresponding dominating sets of G differ by either adding or deleting a single vertex. In this paper we consider and study the n-dominating graph of specific graphs.