The metric dimension of some generalized Petersen graphs
type: Item
instance of: scholarly article
title: The metric dimension of some generalized Petersen graphs
zbMATH Open document ID: 1417.05054
DOI: 10.1155/2018/4531958
author: Zehui Shao
author: Pu Wu
author: Jia-Biao Liu
author: Seyed Mahmood Sheikholeslami
published in: Discrete Dynamics in Nature and Society
publication date: 2019-02-20T00:00:00Z
review text: Summary: The distance \(d(u, v)\) between two distinct vertices \(u\) and \(v\) in a graph \(G\) is the length of a shortest \((u, v)\)-path in \(G\). For an ordered subset \(W = \{w_1, w_2, \ldots, w_k \}\) of vertices and a vertex \(v\) in \(G\), the code of \(v\) with respect to \(W\) is the ordered \(k\)-tuple \(c_W(v) = (d(v, w_1), d(v, w_2), \ldots, d(v, w_k))\). The set \(W\) is a resolving set for \(G\) if every two vertices of \(G\) have distinct codes. The \textit{metric dimension} of \(G\) is the minimum cardinality of a resolving set of \(G\). In this paper, we first extend the results of the metric dimension of \(P(n, 3)\) and \(P(n, 4)\) and study bounds on the metric dimension of the families of the generalized Petersen graphs \(P(2 k, k)\) and \(P(3 k, k)\). The obtained results mean that these families of graphs have constant metric dimension.
Mathematics Subject Classification ID: 05C12
Mathematics Subject Classification ID: 05C75
zbMATH DE Number: 7026585
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2018/4531958
OpenAlex ID: W2886902684
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Wikidata QID: Q129478710
description: scientific article; zbMATH DE number 7026585