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On the Bounded Partition Dimension of Some Generalised Graph Structures

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  • Wajdi Alghamdi
  • Muhammad Ahsan Asim
  • Akbar Ali

Abstract

Consider λ to be a connected graph with a vertex set Vλ 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 Vλ. 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 & Akbar Ali, 2022. "On the Bounded Partition Dimension of Some Generalised Graph Structures," Journal of Mathematics, Hindawi, vol. 2022, pages 1-11, December.
    • Handle: RePEc:hin:jjmath:9531182
    DOI: 10.1155/2022/9531182
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