On Partition Dimension of Some Cycle-Related Graphs. (8th March 2021)

• Record Type: Journal Article
• Authors: Wei, Changcheng; Nadeem, Muhammad Faisal; Afzal Siddiqui, Hafiz Muhammad; Azeem, Muhammad; Liu, Jia-Bao; Khalil, Adnan
• Other Names: Torcicollo Isabella Academic Editor.
• Is Part Of: Mathematical problems in engineering. Volume 2021(2021)
• Publication Date: 2021-03-08
• Subjects: Engineering mathematics -- Periodicals; 510.2462
• DOI: 10.1155/2021/4046909
• Languages: English
• ISSNs: 1024-123X

Abstract

Abstract : Let G be a simple connected graph. Suppose Δ = Δ 1, Δ 2, …, Δ l an l -partition of V G . A partition representation of a vertex α w . r . t Δ is the l − vector d α, Δ 1, d α, Δ 2, …, d α, Δ l, denoted by r α | Δ . Any partition Δ is referred as resolving partition if ∀ α i ≠ α j ∈ V G such that r α i | Δ ≠ r α j | Δ . The smallest integer l is referred as the partition dimension pd G of G if the l -partition Δ is a resolving partition. In this article, we discuss the partition dimension of kayak paddle graph, cycle graph with chord, and a graph generated by chain of cycles. It has been shown that the partition dimension of the said families of graphs is constant.