The edge hop domination number of a graph

Abstract

Let G = (V,E) be a graph. A set S ⊆ E(G) is called an edge hop dominating set if S=E(G) or for every g∈E(G)\S, there exists h∈S such that d(g,h) = 1. The minimum cardinality of an edge hop domination set of G is called the edge hop domination number of G is denoted by γ eh (G). The edge hop domination number of some standard graphs are determined. It is proved that for any two connected graphs H and K of orders n 1 and n 2 respectively, γ eh (H+K)=3. Also it is proved that for any two connected graphs of sizes m 1 ≥3 and m 2 ≥3 respectively, γ eh (H◦K)≤m1.