Bounds on partition dimension of Peterson graphs


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

JOURNAL OF INFORMATION & OPTIMIZATION SCIENCES, 2021 (Peer-Reviewed Journal) identifier

  • Publication Type: Article / Article
  • Publication Date: 2021
  • Doi Number: 10.1080/02522667.2021.1936902
  • Journal Name: JOURNAL OF INFORMATION & OPTIMIZATION SCIENCES
  • Journal Indexes: Emerging Sources Citation Index
  • Keywords: Generalized Peterson graph, Partition dimension, Partition resolving set, Sharp bounds of partition dimension, TOPOLOGICAL INDEXES, METRIC DIMENSION, POLYNOMIALS

Abstract

The distance of a connected, simple graph P is denoted by d(eta(1), eta(2)), which is the length of a shortest path between the vertices eta(1), eta(2) is an element of V(P), where V(P) is the vertex set of P. The l- ordered partition of V(P) is theta = (theta(1), theta(2), ..., theta(t)}. A vertex eta is an element of V(P), and r(eta vertical bar theta) = {d(eta, theta(1)), d(eta, theta(2)), ...., d(eta, theta(t))} be a l - tuple distances, where r(eta vertical bar theta) is the representation of a vertex eta with respect to set theta. If r(eta vertical bar theta) of eta is unique, for every pair of vertices, then theta is the resolving partition set of V(P). The minimum number l in the resolving partition set theta is known as partition dimension (pd(P)). In this paper, we studied the generalized families of Peterson graph, P-lambda,P-lambda-1 and proved that these families have bounded partition dimension.