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 $S$. A Roman dominating function on a graph $G=(V. E)$ is a function $f: V(G) \longrightarrow \{0. 1. https://safeersappliancers.shop/product-category/hisense-rs694n4tf1-american-style-fridge-freezer-black-steel/