Graphs with Large Hop Roman Domination Number
A subset $S$ of vertices of a graph $G$ is a hop dominating set if every vertex outside $S$ is at distance two from a vertex of Washing Machine Hose $S$.A Roman dominating function on a graph $G=(V,E)$ is a function $f: V(G) longrightarrow {0, 1, 2}$ satisfying the condition that every vertex $u$ for which $f(u)=0$ is adjacent to at least one verte