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

Author

Listed:
  • 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)

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.

Suggested Citation

  • Laxman Saha & Mithun Basak & Kalishankar Tiwary & Kinkar Chandra Das & Yilun Shang, 2022. "On the Characterization of a Minimal Resolving Set for Power of Paths," Mathematics, MDPI, vol. 10(14), pages 1-13, July.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:14:p:2445-:d:862037
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    References listed on IDEAS

    as
    1. Jun Guo & Kaishun Wang & Fenggao Li, 2013. "Metric dimension of some distance-regular graphs," Journal of Combinatorial Optimization, Springer, vol. 26(1), pages 190-197, July.
    2. Laxman Saha & Rupen Lama & Kalishankar Tiwary & Kinkar Chandra Das & Yilun Shang, 2022. "Fault-Tolerant Metric Dimension of Circulant Graphs," Mathematics, MDPI, vol. 10(1), pages 1-16, January.
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    Cited by:

    1. Laxman Saha & Rupen Lama & Bapan Das & Avishek Adhikari & Kinkar Chandra Das, 2023. "Optimal Fault-Tolerant Resolving Set of Power Paths," Mathematics, MDPI, vol. 11(13), pages 1-18, June.
    2. Asad Khan & Ghulam Haidar & Naeem Abbas & Murad Ul Islam Khan & Azmat Ullah Khan Niazi & Asad Ul Islam Khan, 2023. "Metric Dimensions of Bicyclic Graphs," Mathematics, MDPI, vol. 11(4), pages 1-17, February.
    3. Laxman Saha & Bapan Das & Kalishankar Tiwary & Kinkar Chandra Das & Yilun Shang, 2023. "Optimal Multi-Level Fault-Tolerant Resolving Sets of Circulant Graph C ( n : 1, 2)," Mathematics, MDPI, vol. 11(8), pages 1-16, April.

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