Resolving set and exchange property in nanotube

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 dou...

Full description

Saved in:
Bibliographic Details
Published inAIMS mathematics Vol. 8; no. 9; pp. 20305 - 20323
Main Authors Koam, Ali N. A., Ali, Sikander, Ahmad, Ali, Azeem, Muhammad, Jamil, Muhammad Kamran
Format Journal Article
LanguageEnglish
Published AIMS Press 01.01.2023
Subjects
exchange property
metric dimension
nanotube
quadrilateral-octogonal grid
resolving set
Online AccessGet full text
ISSN2473-6988
2473-6988
DOI10.3934/math.20231035

Cover

More Information
Summary: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.
ISSN:2473-6988
2473-6988
DOI:10.3934/math.20231035