On 1-movable Strong Resolving Hop Domination in Graphs
DOI:
https://doi.org/10.29020/nybg.ejpam.v16i2.4658Keywords:
Hop Dominating Set, Movable strong resolving dominating setAbstract
A set $S$ is a $1$-\emph{movable strong resolving hop dominating set} of $G$ if for every $v \in S$, either $S \setminus \{v\}$ is a strong resolving hop dominating set or there exists a vertex $u \in (V(G)\setminus S) \cap N_G(v)$ such that $(S \setminus \{v\}) \cap \{u\}$ is a strong resolving hop dominating set of $G$. The minimum cardinality of a $1$-movable strong resolving hop dominating set of $G$ is denoted by $\gamma^{1}_{msRh}(G)$. In this paper, we obtained the corresponding parameter in graphs resulting from the join, corona and lexicographic product of two graphs. Specifically, we characterize the 1-movable strong resolving hop dominating sets in these types of graphs and determine the bounds or exact values of their 1-movable strong resolving hop domination numbers.
Downloads
Published
Issue
Section
License
Copyright (c) 2023 European Journal of Pure and Applied Mathematics
This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License.
Upon acceptance of an article by the European Journal of Pure and Applied Mathematics, the author(s) retain the copyright to the article. However, by submitting your work, you agree that the article will be published under the Creative Commons Attribution-NonCommercial 4.0 International License (CC BY-NC 4.0). This license allows others to copy, distribute, and adapt your work, provided proper attribution is given to the original author(s) and source. However, the work cannot be used for commercial purposes.
By agreeing to this statement, you acknowledge that:
- You retain full copyright over your work.
- The European Journal of Pure and Applied Mathematics will publish your work under the Creative Commons Attribution-NonCommercial 4.0 International License (CC BY-NC 4.0).
- This license allows others to use and share your work for non-commercial purposes, provided they give appropriate credit to the original author(s) and source.