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Research Article | Open Access

Resolving set and exchange property in nanotube

Ali N. A. Koam1Sikander Ali2Ali Ahmad3( )Muhammad Azeem4Muhammad Kamran Jamil4
Department of Mathematics, College of Science, Jazan University, New Campus, Jazan 2097, Saudi Arabia
Department of Mathematics, COMSATS University Islamabad, Sahiwal Campus, Pakistan
Department of Information Technology and Security, College of Computer Science and Information Technology, Jazan University, Jazan, Saudi Arabia
Department of Mathematics, Riphah International University Lahore, Pakistan
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Abstract

Give us a linked graph, G = ( V , E ) . A vertex w V distinguishes between two components (vertices and edges) x , y E V if d G ( w , x ) d G ( w , y ) . Let W 1 and W 2 be two resolving sets and W 1 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.

CLC number: 05C09, 05C12, 05C92

References

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AIMS Mathematics
Pages 20305-20323

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Cite this article:
Koam ANA, Ali S, Ahmad A, et al. Resolving set and exchange property in nanotube. AIMS Mathematics, 2023, 8(9): 20305-20323. https://doi.org/10.3934/math.20231035

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Received: 20 March 2023
Revised: 06 June 2023
Accepted: 12 June 2023
Published: 15 September 2023
©2023 the Author(s), licensee AIMS Press.

This is an open access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0)