On Partition Dimension of Some Cycle-Related Graphs. (8th March 2021) - Wei, Changcheng; Nadeem, Muhammad Faisal; Afzal Siddiqui, Hafiz Muhammad; Azeem, Muhammad; Liu, Jia-Bao; Khalil, Adnan
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.