A Comprehensive Analysis of Clique Vertex Neighborhood Numbers.

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Bibliographic Details
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]
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Database:	Engineering Source

Description
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]
ISSN:	1816093X