On the Characterization of a Minimal Resolving Set for Power of Paths

Laxman Saha, Mithun Basak, Kalishankar Tiwary, Kinkar Chandra Das, Yilun Shang

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Abstract

For a simple connected graph G=(V,E), an ordered set W⊆V, is called a resolving set of G if for every pair of two distinct vertices u and v, there is an element w in W such that d(u,w)≠d(v,w). A metric basis of G is a resolving set of G with minimum cardinality. The metric dimension of G is the cardinality of a metric basis and it is denoted by β(G). In this article, we determine the metric dimension of power of finite paths and characterize all metric bases for the same.
Original languageEnglish
Article number2445
Number of pages13
JournalMathematics
Volume10
Issue number14
DOIs
Publication statusPublished - 13 Jul 2022

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