### Abstract

For every rational number x 2 (0; 1), we construct a pair of graphs one regular and one nonregular with adjacency matrices A1 and A2, having the property that A1-xJ and A2-xJ have the same spectrum (J is the all-ones matrix). This solves a problem of Van Dam and the second author.For some values of x, we have generated the smallest examples (with respect to the number of vertices) by computer.

Original language | English |
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Place of Publication | Tilburg |

Publisher | Operations research |

Number of pages | 6 |

Volume | 2005-124 |

Publication status | Published - 2005 |

### Publication series

Name | CentER Discussion Paper |
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Volume | 2005-124 |

### Keywords

- graphs
- matrices

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## Cite this

Chesnokov, A. A., & Haemers, W. H. (2005).

*Regularity and the Generalized Adjacency Spectra of Graphs*. (CentER Discussion Paper; Vol. 2005-124). Operations research.