Article
Details
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.
Keywords
Main eigenvalue; Minimum degree; Strongly regular graph; Symmetric 2-design; Vertex-deleted subgraph
Journal
Linear Algebra and Its Applications: Volume 507
Status | Published |
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Publication date | 31/12/2016 |
Publication date online | 21/06/2016 |
Date accepted by journal | 17/06/2016 |
URL | http://hdl.handle.net/1893/23940 |
Publisher | Elsevier |
ISSN | 0024-3795 |
People (1)
Emeritus Professor, Mathematics