On the Bounded Partition Dimension of Some Generalised Graph Structures. (5th December 2022)

• Record Type: Journal Article
• Authors: Alghamdi, Wajdi; Asim, Muhammad Ahsan
• Other Names: Ali Akbar Academic Editor.
• Is Part Of: Journal of mathematics. Volume 2022(2022)
• Publication Date: 2022-12-05
• Subjects: Mathematics -- Periodicals; Mathematics; Periodicals; 510
• DOI: 10.1155/2022/9531182
• Languages: English
• ISSNs: 2314-4629

Abstract

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 p d, 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.