Metric dimension of growing infinite graphs
Preprint
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
All Related Versions
This publication has 10 references indexed in Scilit:
- Truncated metric dimension for finite graphsDiscrete Applied Mathematics, 2022
- On the robustness of the metric dimension of grid graphs to adding a single edgeDiscrete Applied Mathematics, 2022
- The threshold strong dimension of a graphDiscrete Mathematics, 2021
- On the k-metric dimension of metric spacesArs Mathematica Contemporanea, 2018
- The effect of vertex or edge deletion on the metric dimension of graphsJournal of Combinatorics, 2015
- On the metric dimension of infinite graphsDiscrete Applied Mathematics, 2012
- On Metric Generators of GraphsMathematics of Operations Research, 2004
- Resolvability in graphs and the metric dimension of a graphDiscrete Applied Mathematics, 2000
- Resolvability and the upper dimension of graphsComputers & Mathematics with Applications, 2000
- Landmarks in graphsDiscrete Applied Mathematics, 1996