$1$-movable $2$-Resolving Hop Domination in Graph
-
Published:2023-07-30
Issue:3
Volume:16
Page:1464-1479
-
ISSN:1307-5543
-
Container-title:European Journal of Pure and Applied Mathematics
-
language:
-
Short-container-title:Eur. J. Pure Appl. Math.
Author:
Mahistrado Angelica Mae,Rara Helen
Abstract
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.
Publisher
New York Business Global LLC
Subject
Applied Mathematics,Geometry and Topology,Numerical Analysis,Statistics and Probability,Algebra and Number Theory,Theoretical Computer Science