Computation of metric dimension and partition dimension of nanotubes

Hafiz Muhammad Afzal Siddiqui, Muhammad Imran

Research output: Contribution to journalArticlepeer-review

14 Citations (Scopus)

Abstract

The partition dimension denoted by pd and metric dimension denoted by dim of a connected graph are related as pd ≤ dim +1. However, the partition dimension may be much smaller than the metric dimension and this phenomena is called a discrepancy between metric dimension and partition dimension. In this paper, we study the metric dimension (location number) and partition dimension of some infinite nanotubes generated by tiling of the plane. We prove that these nanotubes have discrepancy between their metric dimension and partition dimension. It is natural to ask for the characterization of graphs having discrepancies between their metric dimension and partition dimension. It is also shown that there exist induced subgraphs of these nanostructures having metric dimension n as well as having constant metric dimension.

Original languageEnglish
Pages (from-to)199-203
Number of pages5
JournalJournal of Computational and Theoretical Nanoscience
Volume12
Issue number2
DOIs
Publication statusPublished - Feb 1 2015
Externally publishedYes

Keywords

  • Basis
  • Metric Dimension
  • Nanotube
  • Partition Dimension
  • Resolving Set

ASJC Scopus subject areas

  • Chemistry(all)
  • Materials Science(all)
  • Condensed Matter Physics
  • Computational Mathematics
  • Electrical and Electronic Engineering

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