Journal of Combinatorics

Volume 15 (2024)

Number 2

Metric dimension of growing infinite graphs

Pages: 159 – 177

DOI: https://dx.doi.org/10.4310/JOC.2024.v15.n2.a2

Authors

Csaba Biró (Department of Mathematics, University of Louisville, Kentucky, U.S.A.)

Beth Novick (School of Mathematical and Statistical Sciences, Clemson University, Clemson, South Carolina, U.S.A.)

Daniela Olejnikova (School of Mathematical and Statistical Sciences, Clemson University, Clemson, South Carolina, U.S.A.; and Public Health Scotland, Edinburgh, Scotland, United Kingdom)

Abstract

We investigate how the metric dimension of infinite graphs change when we add edges to the graph. Our two main results: (1) there exists a growing sequence of graphs (under the subgraph relation, but without adding vertices) for which the metric dimension changes between finite and infinite infinitely many times; (2) finite changes in the edge set can not change the metric dimension from finite to infinite or vice versa.

Keywords

metric dimension, infinite graph

2010 Mathematics Subject Classification

Primary 05C63. Secondary 05C69.

Full Text (PDF format)

Received 14 May 2022

Accepted 13 March 2023

Published 23 January 2024