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

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...

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Bibliographic Details
Main Authors: Zafar Hussain, Mobeen Munir, Maqbool Chaudhary, Shin Min Kang
Format: Article
Language:English
Published: MDPI AG 2018-07-01
Series:Symmetry
Subjects:
Online Access:http://www.mdpi.com/2073-8994/10/8/300
Description
Summary: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.
ISSN:2073-8994