On the Bounded Partition Dimension of Some Generalised Graph Structures

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 p...

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Bibliographic Details
Main Authors: Wajdi Alghamdi, Muhammad Ahsan Asim
Format: Article
Language:English
Published: Wiley 2022-01-01
Series:Journal of Mathematics
Online Access:http://dx.doi.org/10.1155/2022/9531182
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Summary: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.
ISSN:2314-4785