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Appears in Collections:Computing Science and Mathematics Journal Articles
Peer Review Status: Refereed
Title: Eigenvalue multiplicity in triangle-free graphs
Authors: Rowlinson, Peter
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Keywords: Bipartite graph
Star complement
Strongly regular graph
Triangle-free graph
Issue Date: 15-Mar-2016
Publisher: Elsevier
Citation: Rowlinson P (2016) Eigenvalue multiplicity in triangle-free graphs, Linear Algebra and Its Applications, 493, pp. 484-493.
Abstract: Let G be a connected triangle-free graph of order n>5 with μ∉{−1,0} as an eigenvalue of multiplicity k>1. We show that if d is the maximum degree in G then k≤n−d−1; moreover, if k=n−d−1 then either (a) G is non-bipartite and k≤(μ2+3μ+1)(μ2+2μ−1), with equality only if G is strongly regular, or (b) G is bipartite and k≤d−1, with equality only if G is a bipolar cone. In each case we discuss the extremal graphs that arise.
Type: Journal Article
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Rights: The publisher does not allow this work to be made publicly available in this Repository. Please use the Request a Copy feature at the foot of the Repository record to request a copy directly from the author. You can only request a copy if you wish to use this work for your own research or private study.
Affiliation: Mathematics - CSM Dept

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