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

• Main Authors: Zafar Hussain, Mobeen Munir, Maqbool Chaudhary, Shin Min Kang
• Format: Article
• Language: English
• Published: MDPI AG 2018-07-01
• Series: Symmetry
• Subjects: alpha-boron nanotube; resolving set; metric basis; metric dimension
• Online Access: http://www.mdpi.com/2073-8994/10/8/300

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.