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Appears in Collections:Computing Science and Mathematics Journal Articles
Peer Review Status: Refereed
Title: Star complements and connectivity in finite graphs
Authors: Rowlinson, Peter
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Keywords: Graph
Star complement
Issue Date: Feb-2014
Publisher: Elsevier
Citation: Rowlinson P (2014) Star complements and connectivity in finite graphs, Linear Algebra and Its Applications, 442, pp. 92-98.
Abstract: Let G be a finite graph with H as a star complement for an eigenvalue other than 0 or -1. Let κ(G), δ(G) denote respectively the vertex-connectivity and minimum degree of G. We prove that κ(G) is controlled by δ(G) and κ(H). In particular, for each k∈N there exists a smallest non-negative integer f(k) such that κ(G)⩾k whenever κ(H)⩾k and δ(G)⩾f(k). We show that f(1)=0, f(2)=2, f(3)=3, f(4)=5 and f(5)=7.
Type: Journal Article
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Rights: Published in Linear Algebra and its Applications by Elsevier; Elsevier believes that individual authors should be able to distribute their accepted author manuscripts for their personal voluntary needs and interests, e.g. posting to their websites or their institution’s repository, e-mailing to colleagues. The Elsevier Policy is as follows: Authors retain the right to use the accepted author manuscript for personal use, internal institutional use and for permitted scholarly posting provided that these are not for purposes of commercial use or systematic distribution. An "accepted author manuscript" is the author’s version of the manuscript of an article that has been accepted for publication and which may include any author-incorporated changes suggested through the processes of submission processing, peer review, and editor-author communications.
Affiliation: Mathematics - CSM Dept

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