On the Bounded Partition Dimension of Some Generalised Graph Structures

Wajdi Alghamdi, Muhammad Ahsan Asim and Akbar Ali

Journal of Mathematics, 2022, vol. 2022, 1-11

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.

Date: 2022
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jjmath:9531182

DOI: 10.1155/2022/9531182

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