Complexity (Jan 2021)

Partition Dimension of Generalized Petersen Graph

  • Hassan Raza,
  • Jia-Bao Liu,
  • Muhammad Azeem,
  • Muhammad Faisal Nadeem

DOI
https://doi.org/10.1155/2021/5592476
Journal volume & issue
Vol. 2021

Abstract

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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 Π is the k-vector, that is, ri|Π=di,B1,di,B2,…,di,Bk. The partition Π is 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.