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Partition Dimension of Generalized Peterson and Harary Graphs

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Date

2021

Journal Title

Journal ISSN

Volume Title

Publisher

Abdus Salam School of mathematical Sciences

Abstract

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. © 2021. All Rights Reserved.

Description

Keywords

Generalized Peterson Graph, Harary Graph, Partition Dimension, Partition Resolving Set, Sharp Bounds Of Partition Dimension

Turkish CoHE Thesis Center URL

WoS Q

N/A

Scopus Q

Q2

Source

Journal of Prime Research in Mathematics

Volume

17

Issue

1

Start Page

84

End Page

94