### Abstract

A Deza graph with parameters (n, k, b, a) is a k-regular graph with n vertices such that any two of its vertices have b or a common neighbours, where b ≥ a. In this paper we investigate spectra of Deza graphs. In particular, using the eigenvalues of a Deza graph we determine the eigenvalues of its children. Divisible design graphs are significant cases of Deza graphs. Sufficient conditions for Deza graphs to be divisible design graphs are given, a few families of divisible design graphs are presented and their properties are studied. Our special attention goes to the invertibility of the adjacency matrices of Deza graphs.

Original language | English |
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Number of pages | 12 |

Journal | Linear and Multilinear Algebra |

DOIs | |

Publication status | Published - 7 Feb 2020 |

### Keywords

- Deza children
- Deza graph
- divisible design graph
- nullity
- spectrum of graph
- PARAMETERS N

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## Cite this

*Linear and Multilinear Algebra*. https://doi.org/10.1080/03081087.2020.1723472