On Partition Dimension of Some Cycle-Related Graphs

Abstract

Let G be a simple connected graph. Suppose Δ=Δ1,Δ2,.,Δl an l-partition of VG. A partition representation of a vertex α w.r.t Δ is the l-vector dα,Δ1,dα,Δ2,.,dα,Δl, denoted by rα|Δ. Any partition Δ is referred as resolving partition if ∀αi≠αj∈VG such that rαi|Δ≠rαj|Δ. The smallest integer l is referred as the partition dimension pdG 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.