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

Laxman Saha, Mithun Basak, Kalishankar Tiwary, Kinkar Chandra Das and Yilun Shang
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Laxman Saha: Department of Mathematics, Balurghat College, Dakshin Dinajpur, Balurghat 733101, India
Mithun Basak: Department of Mathematics, Balurghat College, Dakshin Dinajpur, Balurghat 733101, India
Kalishankar Tiwary: Department of Mathematics, Raiganj University, Raiganj 733134, India
Kinkar Chandra Das: Department of Mathematics, Sungkyunkwan University, Suwon 16419, Korea
Yilun Shang: Department of Computer and Information Sciences, Northumbria University, Newcastle NE1 8ST, UK

Mathematics, 2022, vol. 10, issue 14, 1-13

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.

Keywords: graph; code; resolving set; metric dimension (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (3)

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