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标题：A Counter Example For Neighbourhood Number Less Than Edge Covering Number Of a Graph
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作者：Surekha Ravi shankar Bhat ; Ravi shankar Bhat ; Smitha Ganesh Bhat 等
期刊名称：Lecture Notes in Engineering and Computer Science
印刷版ISSN：2078-0958
电子版ISSN：2078-0966
出版年度：2022
卷号：52
期号：2
语种：English
出版社：Newswood and International Association of Engineers
摘要：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 vertexv ∈ V , n-covers an edge x ∈ X if x ∈ hN[v]i , the subgraphinduced by the set N[v]. The n-covering number ρn(G)introduced by Sampathkumar and Neeralagi [18] is theminimum number of vertices needed to n-cover all theedges of G. In this paper one of the results proved in[18] is disproved by exhibiting an infinite class of graphsas counter example. Further, an expression for numberof triangles in any graph is established. In addition, theproperties of clique regular graphs has been studied.
关键词：n-coverings; clique number; independence number; matching number and edge covering number.