Hop Domination in Graphs-II

Let G = (V, E) be a graph. A set S subset of V (G) is a hop dominating set of G if for every v is an element of V - S, there exists u is an element of S such that d(u, v) = 2. The minimum cardinality of a hop dominating set of G is called a hop domination number of G and is denoted by gamma(h)(G). In this paper we characterize the family of trees and unicyclic graphs for which gamma(h)(G) = gamma(t)(G) and gamma(h)(G) = gamma(c)(G) where gamma(t)(G) and gamma(c)(G) are the total domination and connected domination numbers of G respectively. We then present the strong equality of hop domination and hop independent domination numbers for trees. Hop domination numbers of shadow graph and mycielskian graph of graph are also discussed.