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

Authors

  • Angelica Mae Mahistrado MSU-IIT
  • Helen Rara MSU-Iligan Institute of Technology

DOI:

https://doi.org/10.29020/nybg.ejpam.v16i3.4770

Keywords:

1-movable 2-resolving hop dominating set, 1-movable 2-resolving hop domination number, join, corona, edge corona, lexicographic product

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.

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Published

2023-07-30

Issue

Section

Nonlinear Analysis

How to Cite

$1$-movable $2$-Resolving Hop Domination in Graph. (2023). European Journal of Pure and Applied Mathematics, 16(3), 1464-1479. https://doi.org/10.29020/nybg.ejpam.v16i3.4770