STORRE
STORRE: Stirling Online Research Repository
http://hdl.handle.net/1893/23031| 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: | p.rowlinson@stirling.ac.uk |
| Keywords: | Bipartite graph Eigenvalue 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. https://doi.org/10.1016/j.laa.2015.12.012 |
| 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): | http://www.rioxx.net/licenses/under-embargo-all-rights-reserved |
| File | Description | Size | Format | |
|---|---|---|---|---|
| Rowlinson_LAA_2016.pdf | Fulltext - Published Version | 315.85 kB | Adobe PDF | Under 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 https://creativecommons.org/publicdomain/zero/1.0/
If you believe that any material held in STORRE infringes copyright, please contact library@stir.ac.uk providing details and we will remove the Work from public display in STORRE and investigate your claim.