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Partition Dimension of Generalized Petersen Graph

Author

Listed:
  • Hassan Raza
  • Jia-Bao Liu
  • Muhammad Azeem
  • Muhammad Faisal Nadeem
  • Francesco lo iudice

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.

Suggested Citation

  • Hassan Raza & Jia-Bao Liu & Muhammad Azeem & Muhammad Faisal Nadeem & Francesco lo iudice, 2021. "Partition Dimension of Generalized Petersen Graph," Complexity, Hindawi, vol. 2021, pages 1-14, October.
    • Handle: RePEc:hin:complx:5592476
    DOI: 10.1155/2021/5592476
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