TY - JOUR

T1 - A Counter Example For Neighbourhood Number Less Than Edge Covering Number Of a Graph

AU - Bhat, Surekha Ravi shankar

AU - Bhat, Ravi shankar

AU - Bhat, Smitha Ganesh

AU - Vinayaka, Sayinath Udupa Nagara

N1 - Publisher Copyright:
© 2022. IAENG International Journal of Applied Mathematics.All Rights Reserved

PY - 2022

Y1 - 2022

N2 - The open neighbourhood N(v) of a vertex v 2 V; is the set of all vertices adjacent to v. Then N[v] = N(v)[fvg is called the enclave of v. We say that a vertex v 2 V, n-covers an edge x ∈ X if x ∈ {N[v]i}, the subgraph induced by the set N[v]. The n-covering number pn(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.

AB - The open neighbourhood N(v) of a vertex v 2 V; is the set of all vertices adjacent to v. Then N[v] = N(v)[fvg is called the enclave of v. We say that a vertex v 2 V, n-covers an edge x ∈ X if x ∈ {N[v]i}, the subgraph induced by the set N[v]. The n-covering number pn(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.

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M3 - Article

AN - SCOPUS:85131097350

SN - 1992-9978

VL - 52

JO - IAENG International Journal of Applied Mathematics

JF - IAENG International Journal of Applied Mathematics

IS - 2

M1 - IJAM_52_2_29

ER -