A finite vector that represents the distances between a vertex and the vertices of an ordered subset  is the metric representation of a vertex  of a graph. S is called a minimal resolving set if no suitable subset of S provides distinct representations for every vertex of 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.

independent metric dimension, coconut tree, extended jewel graph.

Received: August 28, 2024; Revised: October 9, 2024; Accepted: October 30, 2024; Published: November 29, 2024

How to cite this article: Yasser M. Hausawi, Mohammed El-Meligy, Zaid Alzaid, Olayan Alharbi, Badr Almutairi and Basma Mohamed, Independent metric dimension of coconut tree and extended jewel graph, Advances and Applications in Discrete Mathematics 42(2) (2025), 97-112. https://doi.org/10.17654/0974165825008

This Open Access Article is Licensed under Creative Commons Attribution 4.0 International License

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