On a conjecture about the local metric dimension of graphs
type: Item
instance of: scholarly article
title: On a conjecture about the local metric dimension of graphs
author: Ali Ghalavand
author: Michael A. Henning
author: M. Tavakoli
published in: Graphs and Combinatorics
publication date: 2022-12-23T00:00:00Z
review text: Let \(G\) be a graph of order \(n\) and clique number \(k\). It was conjectured in [\textit{G. Abrishami} et al., Discrete Math. 345, No. 4, Article ID 112763, 10 p. (2022; Zbl 1482.05076)] that the local metric dimension of \(G\) is bounded from the above by \(\frac{k-1}{k}n\). This article proves this conjecture. It is further proved that equality is attained precisely for complete graphs.
reviewed by: Sandi Klavžar
Mathematics Subject Classification ID: 05C12
Mathematics Subject Classification ID: 05C69
Mathematics Subject Classification ID: 05C70
zbMATH DE Number: 7636970
zbMATH Keywords: local metric dimension
zbMATH Keywords: local metric generator
zbMATH Keywords: clique
MaRDI profile type: Publication
full work available at URL: s00373-022-02601-z
OpenAlex ID: W4313448629
Wikidata QID: Q122922712
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DOI: 10.1007/S00373-022-02601-Z
description: scientific article; zbMATH DE number 7636970