Let G = (V, E) be a graph. A set S ⊂ V (G) is a hop dominating set of G if for every v ∈ V − S, there exists u ∈ 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 γ h (G). In this paper we characterize the family of trees and unicyclic graphs for which γ h (G) = γt(G) and γ h (G) = γc(G) where γt(G) and γc(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.
View related articles View Crossmark data Citing articles: 4 View citing articles Please cite this article in press as: D. Sarala, et al., F index of graphs based on four new operations related to the strong product,
Let G = (V, E) be a graph with p vertices and q edges. A subsetThe minimum cardinality of a hop dominating set of G is called a hop domination number of G and is denoted by γ h (G). The subdivision graph S(G) of a graph G is a graph obtained by subdividing every edge of G exactly once. In this paper, we obtain an upper bound on hop domination number of subdivision graph of any connected graph G in terms of number of edges q, the maximum degree ∆(G) and domination number γ(G) of G. We also characterize the family of connected graphs attaining this bound.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.