**Sunny Kumar Sharma and Vijay Kumar Bhat**

Notes on Number Theory and Discrete Mathematics

Print ISSN 1310–5132, Online ISSN 2367–8275

Volume 29, 2023, Number 3, Pages 426–444

DOI: 10.7546/nntdm.2023.29.3.426-444

**Full paper (PDF, 288 Kb)**

## Details

### Authors and affiliations

Sunny Kumar Sharma

*Department of Mathematics, Manipal Institute of Technology Bengaluru,
Manipal Academy of Higher Education, Manipal, Karnataka, India*

Vijay Kumar Bhat

*School of Mathematics, Shri Mata Vaishno Devi University
Katra-182320, Jammu and Kashmir, India*

### Abstract

Let be a non-trivial simple connected graph with edge and vertex set and respectively. A subset with distinct vertices is said to be a vertex resolving set in if for each pair of distinct vertices and in we have for some vertex A resolving set with minimum possible vertices is said to be a metric basis for . The cardinality of metric basis is called the metric dimension of denoted by In this paper, we prove that the metric dimension is constant and equal to for certain closely related families of convex polytopes.

### Keywords

- Resolving set
- Metric dimension
- Nonagonal circular ladder
- Planar graph
- Convex polytopes

### 2020 Mathematics Subject Classification

- 05C12
- 05C76
- 05C90

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### Manuscript history

- Received: 5 April 2021
- Revised: 9 February 2023
- Accepted: 16 June 2023
- Online First: 19 June 2023

### Copyright information

Ⓒ 2023 by the Authors.

This is an Open Access paper distributed under the terms and conditions of the Creative Commons Attribution 4.0 International License (CC BY 4.0).

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## Cite this paper

Sharma, S. K., & Bhat, V. J. (2023). On vertex resolvability of a circular ladder of nonagons. *Notes on Number Theory and Discrete Mathematics*, 29(3), 426-444, DOI: 10.7546/nntdm.2023.29.3.426-444.