Advances and Applications in Discrete Mathematics

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INDEPENDENT METRIC DIMENSION OF COCONUT TREE AND EXTENDED JEWEL GRAPH

Authors

  • Yasser M. Hausawi
  • Mohammed El-Meligy
  • Zaid Alzaid
  • Olayan Alharbi
  • Badr Almutairi
  • Basma Mohamed

Keywords:

independent metric dimension, coconut tree, extended jewel graph

DOI:

https://doi.org/10.17654/0974165825008

Abstract

A finite vector that represents the distances between a vertex $(v)$ and the vertices of an ordered subset $S \subseteq V(G)$ is the metric representation of a vertex $(v)$ of a graph. $S$ is called a minimal resolving set if no suitable subset of $S$ provides distinct representations for every vertex of $V(G)$. The lowest minimal resolving set (in relation to its cardinality) has a cardinality that determines $G$ 's metric dimension. In case $S$ has independent vertices, it can be referred to as an independent resolving set (ir-set). The value of the independent resolving number for different classes of graphs is found and defined. In this study, we investigate the graph classes' independent metric dimension. Our results demonstrate the differences in independent metric dimensions throughout families of graphs.

Received: August 28, 2024
Revised: October 9, 2024
Accepted: October 30, 2024

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Published

2024-11-29

Issue

Vol. 42 No. 2 (2025)

Section

Articles

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How to Cite

INDEPENDENT METRIC DIMENSION OF COCONUT TREE AND EXTENDED JEWEL GRAPH. (2024). Advances and Applications in Discrete Mathematics, 42(2), 97-112. https://doi.org/10.17654/0974165825008

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