Partition Dimension of Generalized Petersen Graph

Hassan Raza, Jia-Bao Liu, Muhammad Azeem, Muhammad Faisal Nadeem and Francesco lo Iudice

Complexity, 2021, vol. 2021, 1-14

Abstract: Let G=VG,EG be the connected graph. For any vertex i∈VG and a subset B⊆VG, the distance between i and B is di;B=mindi,j|j∈B. The ordered k-partition of VG is Π=B1,B2,…,Bk. The representation of vertex i with respect to Πis the k-vector, that is, ri|Π=di,B1,di,B2,…,di,Bk. The partition Πis called the resolving (distinguishing) partition if ri|Π≠rj|Π, for all distinct i,j∈VG. The minimum cardinality of the resolving partition is called the partition dimension, denoted as pdG. In this paper, we consider the upper bound for the partition dimension of the generalized Petersen graph in terms of the cardinalities of its partite sets.

Date: 2021
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Persistent link: https://EconPapers.repec.org/RePEc:hin:complx:5592476

DOI: 10.1155/2021/5592476

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