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On the Bounded Partition Dimension of Some Generalised Graph Structures

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  • Wajdi Alghamdi
  • Muhammad Ahsan Asim

Abstract

Consider λ to be a connected graph with a vertex set V(λ) that may be partitioned into any partition set S. If each vertex in λ has a separate representation with regard to S and is an ordered k partition, then the set with S is a resolving partition of λ.. A partition dimension of λ, represented by pd, is the minimal cardinality of resolving k partitions of V(λ). The partition dimension of various generalised families of graphs, such as the Harary graph, Cayley graph, and Pendent graph, is given as a sharp upper bound in this article.

Suggested Citation

  • Wajdi Alghamdi & Muhammad Ahsan Asim, 2022. "On the Bounded Partition Dimension of Some Generalised Graph Structures," Journal of Mathematics, John Wiley & Sons, vol. 2022(1).
    • Handle: RePEc:wly:jjmath:v:2022:y:2022:i:1:n:9531182
    DOI: 10.1155/2022/9531182
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    References listed on IDEAS

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    1. Hassan Raza & Jia-Bao Liu & Muhammad Azeem & Muhammad Faisal Nadeem & Francesco lo iudice, 2021. "Partition Dimension of Generalized Petersen Graph," Complexity, Hindawi, vol. 2021, pages 1-14, October.
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