$1$-movable $2$-Resolving Hop Domination in Graph

Let $G$ be a connected graph. A set $S$ of vertices in is 1-movable 2-resolving hop dominating if and for every $v \in S$, either $S\backslash \{v\}$ or there exists vertex $u \big((V (G) \backslash S) \cap N_G(v)\big)$ such that $\big(S \{v\}\big) \cup \{u\}$ $G$. The domination number $G$, denoted by $\gamma^{1}_{m2Rh}(G)$ the smallest cardinality In this paper, we investigate concept study it graphs resulting from some binary operations. Specifically, characterize sets join, corona lexicographic products graphs, determine bounds each these graphs.