Computing Edge Metric Dimension of One-Pentagonal Carbon Nanocone

Minimum resolving sets (edge or vertex) have become an integral part of molecular topology and combinatorial chemistry. Resolving sets for a specific network provide crucial information required for the identification of each item contained in the network, uniquely. The distance between an edge e =...

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Autores principales:	Sunny Kumar Sharma, Hassan Raza, Vijay Kumar Bhat
Formato:	article
Lenguaje:	EN
Publicado:	Frontiers Media S.A. 2021
Materias:	one-pentagonal carbon nonacone metric dimension resolving set edge metric dimension molecular graph Physics QC1-999
Acceso en línea:	https://doaj.org/article/ab429ad7a12a4d0788ca3e99ddf5fb44
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spelling	oai:doaj.org-article:ab429ad7a12a4d0788ca3e99ddf5fb442021-11-18T09:32:55ZComputing Edge Metric Dimension of One-Pentagonal Carbon Nanocone2296-424X10.3389/fphy.2021.749166https://doaj.org/article/ab429ad7a12a4d0788ca3e99ddf5fb442021-11-01T00:00:00Zhttps://www.frontiersin.org/articles/10.3389/fphy.2021.749166/fullhttps://doaj.org/toc/2296-424XMinimum resolving sets (edge or vertex) have become an integral part of molecular topology and combinatorial chemistry. Resolving sets for a specific network provide crucial information required for the identification of each item contained in the network, uniquely. The distance between an edge e = cz and a vertex u is defined by d(e, u) = min{d(c, u), d(z, u)}. If d(e1, u) ≠ d(e2, u), then we say that the vertex u resolves (distinguishes) two edges e1 and e2 in a connected graph G. A subset of vertices RE in G is said to be an edge resolving set for G, if for every two distinct edges e1 and e2 in G we have d(e1, u) ≠ d(e2, u) for at least one vertex u ∈ RE. An edge metric basis for G is an edge resolving set with minimum cardinality and this cardinality is called the edge metric dimension edim(G) of G. In this article, we determine the edge metric dimension of one-pentagonal carbon nanocone (1-PCNC). We also show that the edge resolving set for 1-PCNC is independent.Sunny Kumar SharmaHassan RazaVijay Kumar BhatFrontiers Media S.A.articleone-pentagonal carbon nonaconemetric dimensionresolving setedge metric dimensionmolecular graphPhysicsQC1-999ENFrontiers in Physics, Vol 9 (2021)
institution	DOAJ
collection	DOAJ
language	EN
topic	one-pentagonal carbon nonacone metric dimension resolving set edge metric dimension molecular graph Physics QC1-999
spellingShingle	one-pentagonal carbon nonacone metric dimension resolving set edge metric dimension molecular graph Physics QC1-999 Sunny Kumar Sharma Hassan Raza Vijay Kumar Bhat Computing Edge Metric Dimension of One-Pentagonal Carbon Nanocone
description	Minimum resolving sets (edge or vertex) have become an integral part of molecular topology and combinatorial chemistry. Resolving sets for a specific network provide crucial information required for the identification of each item contained in the network, uniquely. The distance between an edge e = cz and a vertex u is defined by d(e, u) = min{d(c, u), d(z, u)}. If d(e1, u) ≠ d(e2, u), then we say that the vertex u resolves (distinguishes) two edges e1 and e2 in a connected graph G. A subset of vertices RE in G is said to be an edge resolving set for G, if for every two distinct edges e1 and e2 in G we have d(e1, u) ≠ d(e2, u) for at least one vertex u ∈ RE. An edge metric basis for G is an edge resolving set with minimum cardinality and this cardinality is called the edge metric dimension edim(G) of G. In this article, we determine the edge metric dimension of one-pentagonal carbon nanocone (1-PCNC). We also show that the edge resolving set for 1-PCNC is independent.
format	article
author	Sunny Kumar Sharma Hassan Raza Vijay Kumar Bhat
author_facet	Sunny Kumar Sharma Hassan Raza Vijay Kumar Bhat
author_sort	Sunny Kumar Sharma
title	Computing Edge Metric Dimension of One-Pentagonal Carbon Nanocone
title_short	Computing Edge Metric Dimension of One-Pentagonal Carbon Nanocone
title_full	Computing Edge Metric Dimension of One-Pentagonal Carbon Nanocone
title_fullStr	Computing Edge Metric Dimension of One-Pentagonal Carbon Nanocone
title_full_unstemmed	Computing Edge Metric Dimension of One-Pentagonal Carbon Nanocone
title_sort	computing edge metric dimension of one-pentagonal carbon nanocone
publisher	Frontiers Media S.A.
publishDate	2021
url	https://doaj.org/article/ab429ad7a12a4d0788ca3e99ddf5fb44
work_keys_str_mv	AT sunnykumarsharma computingedgemetricdimensionofonepentagonalcarbonnanocone AT hassanraza computingedgemetricdimensionofonepentagonalcarbonnanocone AT vijaykumarbhat computingedgemetricdimensionofonepentagonalcarbonnanocone
_version_	1718420921089261568

Computing Edge Metric Dimension of One-Pentagonal Carbon Nanocone

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