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http://hdl.handle.net/1893/23940| Appears in Collections: | Computing Science and Mathematics Journal Articles |
| Peer Review Status: | Refereed |
| Title: | On graphs with just three distinct eigenvalues |
| Author(s): | Rowlinson, Peter |
| Contact Email: | pr@maths.stir.ac.uk |
| Keywords: | Main eigenvalue Minimum degree Strongly regular graph Symmetric 2-design Vertex-deleted subgraph |
| Issue Date: | 2016 |
| Date Deposited: | 1-Aug-2016 |
| Citation: | Rowlinson P (2016) On graphs with just three distinct eigenvalues. Linear Algebra and Its Applications, 507, pp. 462-473. https://doi.org/10.1016/j.laa.2016.06.031 |
| Abstract: | Let G be a connected non-bipartite graph with exactly three distinct eigenvalues Rho, mu, lambda, where Rho >mu >lambda. In the case that G has just one non-main eigenvalue, we find necessary and sufficient spectral conditions on a vertex-deleted subgraph of G for G to be the cone over a strongly regular graph. Secondly, we determine the structure of G when just mu is non-main and the minimum degree of G is 1 + mu − lambda mu: such a graph is a cone over a strongly regular graph, or a graph derived from a symmetric 2-design, or a graph of one further type. |
| DOI Link: | 10.1016/j.laa.2016.06.031 |
| Rights: | During the embargo use Request a Copy at the foot of the record. You can only request a copy to use for your own research or private study. Published in Linear Algebra and Its Applications by Elsevier; Elsevier believes that individual authors should be able to distribute their AAMs for their personal voluntary needs and interests, e.g. posting to their websites or their institution’s repository, e-mailing to colleagues. However, our policies differ regarding the systematic aggregation or distribution of AAMs to ensure the sustainability of the journals to which AAMs are submitted. Therefore, deposit in, or posting to, subject-oriented or centralized repositories (such as PubMed Central), or institutional repositories with systematic posting mandates is permitted only under specific agreements between Elsevier and the repository, agency or institution, and only consistent with the publisher’s policies concerning such repositories. Voluntary posting of AAMs in the arXiv subject repository is permitted. |
Files in This Item:
| File | Description | Size | Format | |
|---|---|---|---|---|
| Three6.pdf | Fulltext - Accepted Version | 272.03 kB | Adobe PDF | View/Open |
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