Open Access

ARTICLE

Metric Identification of Vertices in Polygonal Cacti

by Xiujun Zhang¹, Muhammad Salman², Anam Rani³, Rashna Tanveer², Usman Ali^3,*, 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

Received 24 June 2022; Accepted 14 September 2022; Issue published 05 January 2023

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.

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Keywords

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