Punjab University Journal of Mathematics, Vol 55, No 3 (2023)

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On the partition dimension of circulant graph Cn(1, 2, 3, 4)

Asim Nadeem, Kamran Azhar, Sohail Zafar, Agha Kashif, Zohaib Zahid

Abstract


Let Λ = {B1,B2, . . . ,Bl} be an ordered l-partition of a connectedgraph G(V (G),E(G)). The partition representation of vertex x withrespect to Λ is the l-vector, r(x|Λ) = (d(x,B1), d(x,B2), . . . , d(x,Bl)), whered(x,B) = min{d(x, y)|y ∈ B} is the distance between x and B. If the l -vectors r(x|Λ), for all x ∈ V (G) are distinct then l - partition is called aresolving partition. The least value of l for which there is a resolving l - partitionis known as the partition dimension of G symbolized as pd(G). In thispaper, the partition dimension of circulant graphs Cn(1, 2, 3, 4) is computedfor n ≥ 8 as,

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