Please use this identifier to cite or link to this item:
Appears in Collections:Computing Science and Mathematics Journal Articles
Peer Review Status: Refereed
Title: Eigenvalue multiplicity in triangle-free graphs
Author(s): Rowlinson, Peter
Contact Email:
Keywords: Bipartite graph
Star complement
Strongly regular graph
Triangle-free graph
Issue Date: 15-Mar-2016
Date Deposited: 5-Apr-2016
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.
DOI Link: 10.1016/j.laa.2015.12.012
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.
Licence URL(s):

Files in This Item:
File Description SizeFormat 
Rowlinson_LAA_2016.pdfFulltext - Published Version315.85 kBAdobe PDFUnder Embargo until 2999-12-30    Request a copy

Note: If any of the files in this item are currently embargoed, you can request a copy directly from the author by clicking the padlock icon above. However, this facility is dependent on the depositor still being contactable at their original email address.

This item is protected by original copyright

Items in the Repository are protected by copyright, with all rights reserved, unless otherwise indicated.

The metadata of the records in the Repository are available under the CC0 public domain dedication: No Rights Reserved

If you believe that any material held in STORRE infringes copyright, please contact providing details and we will remove the Work from public display in STORRE and investigate your claim.