@article{Mahistrado_Rara_2023, title={$1$-movable $2$-Resolving Hop Domination in Graph}, volume={16}, url={https://ejpam.com/index.php/ejpam/article/view/4770}, DOI={10.29020/nybg.ejpam.v16i3.4770}, abstractNote={<div>Let $G$ be a connected graph. A set $S$ of vertices in $G$ is a 1-movable 2-resolving hop dominating set of $G$ if $S$ is a 2-resolving hop dominating set in $G$ and for every $v \in S$, either $S\backslash \{v\}$ is a 2-resolving hop dominating set of $G$ or there exists a vertex $u \in \big((V (G) \backslash S) \cap N_G(v)\big)$ such that $\big(S \backslash \{v\}\big) \cup \{u\}$ is a 2-resolving hop dominating set of $G$. The 1-movable 2-resolving hop domination number of $G$, denoted by $\gamma^{1}_{m2Rh}(G)$ is the smallest cardinality of a 1-movable 2-resolving hop dominating set of $G$. In this paper, we investigate the concept and study it for graphs resulting from some binary operations. Specifically, we characterize the 1-movable 2-resolving hop dominating sets in the join, corona and lexicographic products of graphs, and determine the bounds of the 1-movable 2-resolving hop domination number of each of these graphs.</div>}, number={3}, journal={European Journal of Pure and Applied Mathematics}, author={Mahistrado, Angelica Mae and Rara, Helen}, year={2023}, month={Jul.}, pages={1464–1479} }