### Abstract

Original language | English |
---|---|

Pages (from-to) | 245-250 |

Journal | Linear Algebra and its Applications |

Volume | 458 |

Early online date | 24 Jun 2014 |

DOIs | |

Publication status | Published - 1 Oct 2014 |

### Fingerprint

### Keywords

- Distance-regular graphs
- spectral excess theorem
- Laplacian spectrum
- orthogonal polynomials

### Cite this

*Linear Algebra and its Applications*,

*458*, 245-250. https://doi.org/10.1016/j.laa.2014.06.001

}

*Linear Algebra and its Applications*, vol. 458, pp. 245-250. https://doi.org/10.1016/j.laa.2014.06.001

**The Laplacian spectral excess theorem for distance-regular graphs.** / van Dam, E.R.; Fiol, M.A.

Research output: Contribution to journal › Article › Scientific › peer-review

TY - JOUR

T1 - The Laplacian spectral excess theorem for distance-regular graphs

AU - van Dam, E.R.

AU - Fiol, M.A.

PY - 2014/10/1

Y1 - 2014/10/1

N2 - The spectral excess theorem states that, in a regular graph Γ, the average excess, which is the mean of the numbers of vertices at maximum distance from a vertex, is bounded above by the spectral excess (a number that is computed by using the adjacency spectrum of Γ), and Γ is distance-regular if and only if equality holds. In this note we prove the corresponding result by using the Laplacian spectrum without requiring regularity of Γ.

AB - The spectral excess theorem states that, in a regular graph Γ, the average excess, which is the mean of the numbers of vertices at maximum distance from a vertex, is bounded above by the spectral excess (a number that is computed by using the adjacency spectrum of Γ), and Γ is distance-regular if and only if equality holds. In this note we prove the corresponding result by using the Laplacian spectrum without requiring regularity of Γ.

KW - Distance-regular graphs

KW - spectral excess theorem

KW - Laplacian spectrum

KW - orthogonal polynomials

U2 - 10.1016/j.laa.2014.06.001

DO - 10.1016/j.laa.2014.06.001

M3 - Article

VL - 458

SP - 245

EP - 250

JO - Linear Algebra and its Applications

JF - Linear Algebra and its Applications

SN - 0024-3795

ER -