Metric Dimension of Some Generalized Families of Toeplitz Graphs-Reference-Cited by-同舟云学术

Metric Dimension of Some Generalized Families of Toeplitz Graphs

Published:2022-03-12 Issue: Volume:2022 Page:1-10
ISSN:1563-5147
Container-title:Mathematical Problems in Engineering
language:en
Short-container-title:Mathematical Problems in Engineering

Author:

Nadeem Muhammad Faisal¹^ORCID,Qu Shaojian²^ORCID,Ahmad Ali³^ORCID,Azeem Muhammad⁴^ORCID

Affiliation:

1. Department of Mathematics, COMSATS University Islamabad Lahore Campus, Lahore 54000, Pakistan

2. University of Shanghai for Science and Technology, Shanghai, China

3. College of Computer Science & Information Technology, Jazan University, Jazan, Saudi Arabia

4. Department of Mathematics, Riphah Institute of Computing and Applied Sciences, Riphah International University, Lahore, Pakistan

Abstract

The metric dimension of a graph

G

is the selection of the minimum possible number of vertices such that each vertex of the graph

G

is distinctively defined by its vector of distances to the set of selected vertices. It was proved that the problem of determining the metric dimension of a graph is NP-hard. In this paper, the metric dimension of Toeplitz graphs with two and three generators is discussed and the exact values are found. Also, two conjectures about the exact metric dimension of Toeplitz graphs are given.

Publisher

Hindawi Limited

Subject

General Engineering,General Mathematics

Link

http://downloads.hindawi.com/journals/mpe/2022/9155291.pdf

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