A Comprehensive Analysis of Clique Vertex Neighborhood Numbers.
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| Title: | A Comprehensive Analysis of Clique Vertex Neighborhood Numbers. |
|---|---|
| Authors: | J. B., Swarna1 swarnajb366@gmail.com, Bhat, K. Arathi2 arathi.bhat@manipal.edu, Bhat, Smitha Ganesh2 smitha.holla@manipal.edu |
| Source: | Engineering Letters. Nov2025, Vol. 33 Issue 11, p4415-4421. 7p. |
| Subjects: | Subgraphs, Mathematical bounds, Graph theory, Statistical models, Geometric vertices, Cardinal numbers |
| Abstract: | The open neighborhood N(w) of a vertex w ∈ V consists of all vertices adjacent to w in an undirected graph. The closed neighborhood N[w], includes w and all vertices reachable from it. A complete maximal subgraph of G is a clique. A clique k ∈ K(G) cv-covers a vertex v if v ∈ 〈N[k]〉, where 〈N[k]〉 is the subgraph induced by the closed neighborhood of k. A set S K(G) is a cv-neighborhood set if every vertex v is cv-covered by some k ∈ S, that is, G = S k∈K(G) 〈N[k]〉. The minimum cardinality of such a set is the clique vertex neighborhood number ncv(G). In this paper, we establish bounds for ncv, characterize graphs attaining these bounds, and compute ncv for various graph products. [ABSTRACT FROM AUTHOR] |
| Copyright of Engineering Letters is the property of International Association of Engineers (IAENG) and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.) | |
| Database: | Engineering Source |
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| Items | – Name: Title Label: Title Group: Ti Data: A Comprehensive Analysis of Clique Vertex Neighborhood Numbers. – Name: Author Label: Authors Group: Au Data: <searchLink fieldCode="AR" term="%22J%2E+B%2E%2C+Swarna%22">J. B., Swarna</searchLink><relatesTo>1</relatesTo><i> swarnajb366@gmail.com</i><br /><searchLink fieldCode="AR" term="%22Bhat%2C+K%2E+Arathi%22">Bhat, K. Arathi</searchLink><relatesTo>2</relatesTo><i> arathi.bhat@manipal.edu</i><br /><searchLink fieldCode="AR" term="%22Bhat%2C+Smitha+Ganesh%22">Bhat, Smitha Ganesh</searchLink><relatesTo>2</relatesTo><i> smitha.holla@manipal.edu</i> – Name: TitleSource Label: Source Group: Src Data: <searchLink fieldCode="JN" term="%22Engineering+Letters%22">Engineering Letters</searchLink>. Nov2025, Vol. 33 Issue 11, p4415-4421. 7p. – Name: Subject Label: Subjects Group: Su Data: <searchLink fieldCode="DE" term="%22Subgraphs%22">Subgraphs</searchLink><br /><searchLink fieldCode="DE" term="%22Mathematical+bounds%22">Mathematical bounds</searchLink><br /><searchLink fieldCode="DE" term="%22Graph+theory%22">Graph theory</searchLink><br /><searchLink fieldCode="DE" term="%22Statistical+models%22">Statistical models</searchLink><br /><searchLink fieldCode="DE" term="%22Geometric+vertices%22">Geometric vertices</searchLink><br /><searchLink fieldCode="DE" term="%22Cardinal+numbers%22">Cardinal numbers</searchLink> – Name: Abstract Label: Abstract Group: Ab Data: The open neighborhood N(w) of a vertex w ∈ V consists of all vertices adjacent to w in an undirected graph. The closed neighborhood N[w], includes w and all vertices reachable from it. A complete maximal subgraph of G is a clique. A clique k ∈ K(G) cv-covers a vertex v if v ∈ 〈N[k]〉, where 〈N[k]〉 is the subgraph induced by the closed neighborhood of k. A set S K(G) is a cv-neighborhood set if every vertex v is cv-covered by some k ∈ S, that is, G = S k∈K(G) 〈N[k]〉. The minimum cardinality of such a set is the clique vertex neighborhood number ncv(G). In this paper, we establish bounds for ncv, characterize graphs attaining these bounds, and compute ncv for various graph products. [ABSTRACT FROM AUTHOR] – Name: AbstractSuppliedCopyright Label: Group: Ab Data: <i>Copyright of Engineering Letters is the property of International Association of Engineers (IAENG) and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.) |
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| RecordInfo | BibRecord: BibEntity: Languages: – Code: eng Text: English PhysicalDescription: Pagination: PageCount: 7 StartPage: 4415 Subjects: – SubjectFull: Subgraphs Type: general – SubjectFull: Mathematical bounds Type: general – SubjectFull: Graph theory Type: general – SubjectFull: Statistical models Type: general – SubjectFull: Geometric vertices Type: general – SubjectFull: Cardinal numbers Type: general Titles: – TitleFull: A Comprehensive Analysis of Clique Vertex Neighborhood Numbers. Type: main BibRelationships: HasContributorRelationships: – PersonEntity: Name: NameFull: J. B., Swarna – PersonEntity: Name: NameFull: Bhat, K. Arathi – PersonEntity: Name: NameFull: Bhat, Smitha Ganesh IsPartOfRelationships: – BibEntity: Dates: – D: 01 M: 11 Text: Nov2025 Type: published Y: 2025 Identifiers: – Type: issn-print Value: 1816093X Numbering: – Type: volume Value: 33 – Type: issue Value: 11 Titles: – TitleFull: Engineering Letters Type: main |
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