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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
Author(s): Rowlinson, Peter
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Keywords: Main eigenvalue
Minimum degree
Strongly regular graph
Symmetric 2-design
Vertex-deleted subgraph
Issue Date: 2016
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.
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