Next Article in Journal
Evaluating Water Use Efficiency in China’s Western Provinces Based on a Slacks-Based Measure (SBM)-Undesirable Window Model and a Malmquist Productivity Index
Next Article in Special Issue
On the Distinguishing Number of Functigraphs
Previous Article in Journal
Game-Theoretic Solutions for Data Offloading in Next Generation Networks
Previous Article in Special Issue
Hyperbolicity of Direct Products of Graphs
Article Menu
Issue 8 (August) cover image

Export Article

Open AccessArticle
Symmetry 2018, 10(8), 300; https://doi.org/10.3390/sym10080300

Computing Metric Dimension and Metric Basis of 2D Lattice of Alpha-Boron Nanotubes

1
Department of Mathematics and Statistics, the University of Lahore, Lahore 54000, Pakistan
2
Division of Science and Technology, University of Education, Lahore 54000, Pakistan
3
Department of Mathematics and RINS, Gyeongsang National University, Jinju 52828, Korea
4
Center for General Education, China Medical University, Taichung 40402, Taiwan
*
Authors to whom correspondence should be addressed.
Received: 16 June 2018 / Revised: 15 July 2018 / Accepted: 19 July 2018 / Published: 25 July 2018
(This article belongs to the Special Issue Symmetry in Graph Theory)
Full-Text   |   PDF [1503 KB, uploaded 25 July 2018]   |  

Abstract

Concepts of resolving set and metric basis has enjoyed a lot of success because of multi-purpose applications both in computer and mathematical sciences. For a connected graph G(V,E) a subset W of V(G) is a resolving set for G if every two vertices of G have distinct representations with respect to W. A resolving set of minimum cardinality is called a metric basis for graph G and this minimum cardinality is known as metric dimension of G. Boron nanotubes with different lattice structures, radii and chirality’s have attracted attention due to their transport properties, electronic structure and structural stability. In the present article, we compute the metric dimension and metric basis of 2D lattices of alpha-boron nanotubes. View Full-Text
Keywords: alpha-boron nanotube; resolving set; metric basis; metric dimension alpha-boron nanotube; resolving set; metric basis; metric dimension
Figures

Figure 1

This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited (CC BY 4.0).
SciFeed

Share & Cite This Article

MDPI and ACS Style

Hussain, Z.; Munir, M.; Chaudhary, M.; Kang, S.M. Computing Metric Dimension and Metric Basis of 2D Lattice of Alpha-Boron Nanotubes. Symmetry 2018, 10, 300.

Show more citation formats Show less citations formats

Note that from the first issue of 2016, MDPI journals use article numbers instead of page numbers. See further details here.

Related Articles

Article Metrics

Article Access Statistics

1

Comments

[Return to top]
Symmetry EISSN 2073-8994 Published by MDPI AG, Basel, Switzerland RSS E-Mail Table of Contents Alert
Back to Top