Resolving set and exchange property in nanotube

Abstract

<abstract><p>Give us a linked graph, $ G = (V, E). $ A vertex $ w\in V $ distinguishes between two components (vertices and edges) $ x, y\in E\cup V $ if $ d_G(w, x)\neq d_G (w, y). $ Let $ W_{1} $ and $ W_{2} $ be two resolving sets and $ W_{1} $ $ \neq $ $ W_{2} $. Then, we can say that the graph $ G $ has double resolving set. A nanotube derived from an quadrilateral-octagonal grid belongs to essential and extensively studied compounds in materials science. Nano-structures are very important due to their thickness. In this article, we have discussed the metric dimension of the graphs of nanotubes derived from the quadrilateral-octagonal grid. We proved that the generalized nanotube derived from quadrilateral-octagonal grid have three metric dimension. We also check that the exchange property is also held for this structure.</p></abstract>

Double edge resolving set and exchange property for nanosheet structure

“…Due to the vast range of applications for which it is put, the concept of edge metric dimension is usually used to solve complex problems. Resolving set and exchange property in nanotube discussed in [26] . The metric dimensions of various chemical structures have been studied in numerous articles.…”