### Abstract

A graph G has constant u = u(G) if any two vertices that are not adjacent have u common neighbours. G has constant u and u if G has constant u = u(G), and its complement G has constant u = u(G). If such a graph is regular, then it is strongly regular, otherwise precisely two vertex degrees occur. We shall prove that a graph has constant u and u if and only if it has two distinct restricted Laplace eigenvalues. Bruck-Ryser type conditions are found. Several constructions are given and characterized. A list of feasible parameter sets for graphs with at most 40 vertices is generated.

Original language | English |
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Publisher | Unknown Publisher |

Number of pages | 14 |

Volume | FEW 688 |

Publication status | Published - 1995 |

### Publication series

Name | Research memorandum / Tilburg University, Faculty of Economics and Business Administration |
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Volume | FEW 688 |

### Keywords

- Graphs
- Eigenvalues
- mathematics

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## Cite this

van Dam, E. R., & Haemers, W. H. (1995).

*Graphs with constant μ and μ*. (Research memorandum / Tilburg University, Faculty of Economics and Business Administration; Vol. FEW 688). Unknown Publisher.