A Counter Example For Neighbourhood Number Less Than Edge Covering Number Of a Graph

Bhat, Surekha R and Bhat, Ravishankar S and Bhat, Smitha and Udupa, Sayinath (2022) A Counter Example For Neighbourhood Number Less Than Edge Covering Number Of a Graph. IAENG International Journal of Applied Mathematics, 52 (2). ISSN 1992-9978

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Abstract

The open neighbourhood N(v) of a vertex v ∈ V, is the set of all vertices adjacent to v. Then N[v] = N(v)∪ {v} is called the enclave of v. We say that a vertex v ∈ V , n-covers an edge x ∈ X if x ∈ hN[v]i, the subgraph induced by the set N[v]. The n-covering number ρn(G) introduced by Sampathkumar and Neeralagi [18] is the minimum number of vertices needed to n-cover all the edges of G. In this paper one of the results proved in [18] is disproved by exhibiting an infinite class of graphs as counter example. Further, an expression for number of triangles in any graph is established. In addition, the properties of clique regular graphs has been studied. Index Terms- n-coverings, clique number, indepen�dence number, matching number and edge covering number.

Item Type: Article
Uncontrolled Keywords: - n-coverings, clique number, indepen�dence number, matching number and edge covering number
Subjects: Engineering > MIT Manipal > Mathematics
Depositing User: MIT Library
Date Deposited: 08 Aug 2022 07:05
Last Modified: 08 Aug 2022 07:05
URI: http://eprints.manipal.edu/id/eprint/159046

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