Partition dimension of generalized Peterson and Harary graphs


Khalaf A. J. M., Nadeem M. F., Azeem M., Farahani M. R., Cancan M.

Journal of Prime Research in Mathematics, vol.17, no.1, pp.84-94, 2021 (Scopus) identifier

  • Publication Type: Article / Article
  • Volume: 17 Issue: 1
  • Publication Date: 2021
  • Journal Name: Journal of Prime Research in Mathematics
  • Journal Indexes: Scopus, Academic Search Premier, zbMATH
  • Page Numbers: pp.84-94
  • Keywords: Generalized Peterson graph, Harary Graph, partition dimension, partition resolving set, sharp bounds of partition dimension
  • Van Yüzüncü Yıl University Affiliated: Yes

Abstract

© 2021. All Rights Reserved.The distance of a connected, simple graph (Formula presented) is denoted by d(α1, α2), which is the length of a shortest path between the vertices α1,α2 (Formula presented) V((Formula presented)), where V((Formula presented)) is the vertex set of (Formula presented). The l-ordered partition of V((Formula presented)) is K = {K1, K2,..., Kl}. A vertex α (Formula presented) V((Formula presented)), and r(α|K) = {d(α, K1), d(α, K2),..., d(α, Kl)} be a l-tuple distances, where r(α|K) is the representation of a vertex a with respect to set K. If r(a|K) of a is unique, for every pair of vertices, then K is the resolving partition set of V((Formula presented)). The minimum number l in the resolving partition set K is known as partition dimension (pd(P)). In this paper, we studied the generalized families of Peterson graph, Pλx and proved that these families have bounded partition dimension.