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# Metric Identification of Vertices in Polygonal Cacti

Xiujun Zhang1, Muhammad Salman2, Anam Rani3, Rashna Tanveer2, Usman Ali3,*, Zehui Shao4

1 School of Computer Science, Chengdu University, Chengdu, China
2 Department of Mathematics, The Islamia University of Bahawalpur, Bahawalpur, Pakistan
3 Centre for Advanced Studies in Pure and Applied Mathematics, Bahauddin Zakariya University, Multan, Pakistan
4 Institute for Intelligent Information Processing, South China Business College of Guangdong University of Foreign Studies, Guangzhou, China

* Corresponding Author: Usman Ali. Email:

(This article belongs to the Special Issue: Resolvability Parameters and their Applications)

Computer Modeling in Engineering & Sciences 2023, 136(1), 883-899. https://doi.org/10.32604/cmes.2023.025162

## Abstract

The distance between two vertices u and v in a connected graph G is the number of edges lying in a shortest path (geodesic) between them. A vertex x of G performs the metric identification for a pair (u, v) of vertices in G if and only if the equality between the distances of u and v with x implies that u = v (That is, the distance between u and x is different from the distance between v and x). The minimum number of vertices performing the metric identification for every pair of vertices in G defines the metric dimension of G. In this paper, we perform the metric identification of vertices in two types of polygonal cacti: chain polygonal cactus and star polygonal cactus.

## Cite This Article

APA Style
Zhang, X., Salman, M., Rani, A., Tanveer, R., Ali, U. et al. (2023). Metric identification of vertices in polygonal cacti. Computer Modeling in Engineering & Sciences, 136(1), 883-899. https://doi.org/10.32604/cmes.2023.025162
Vancouver Style
Zhang X, Salman M, Rani A, Tanveer R, Ali U, Shao Z. Metric identification of vertices in polygonal cacti. Comput Model Eng Sci. 2023;136(1):883-899 https://doi.org/10.32604/cmes.2023.025162
IEEE Style
X. Zhang, M. Salman, A. Rani, R. Tanveer, U. Ali, and Z. Shao "Metric Identification of Vertices in Polygonal Cacti," Comput. Model. Eng. Sci., vol. 136, no. 1, pp. 883-899. 2023. https://doi.org/10.32604/cmes.2023.025162

This work is licensed under a Creative Commons Attribution 4.0 International License , which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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