Research output

Article in Journal ()

**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.

**Keywords**

Main eigenvalue; Minimum degree; Strongly regular graph; Symmetric 2-design; Vertex-deleted subgraph

Status | Published |
---|---|

Authors | Rowlinson Peter |

Publication date | 2016 |

Publication date online | 21/06/2016 |

Date accepted by journal | 17/06/2016 |

Publisher | Elsevier |

ISSN | 0024-3795 |

Language | English |

**Journal**

Linear Algebra and its Applications: Volume 507 (2016)