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Appears in Collections:Computing Science and Mathematics Journal Articles
Peer Review Status: Refereed
Title: On graphs with just three distinct eigenvalues
Authors: Rowlinson, Peter
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Keywords: Main eigenvalue
Minimum degree
Strongly regular graph
Symmetric 2-design
Vertex-deleted subgraph
Issue Date: 2016
Publisher: Elsevier
Citation: Rowlinson P (2016) On graphs with just three distinct eigenvalues, Linear Algebra and Its Applications, 507, pp. 462-473.
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.
Type: Journal Article
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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.
Affiliation: Mathematics - CSM Dept

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