### Abstract

*m*-partially distance-regular graphs and

*j*-punctually eigenspace distance-regular graphs by using their spectra. Our results can also be seen as a generalization of the so-called spectral excess theorem for distance-regular graphs, and they lead to a dual version of it.

Original language | English |
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Pages (from-to) | 2730-2734 |

Journal | Discrete Mathematics |

Volume | 312 |

Issue number | 17 |

DOIs | |

Publication status | Published - Sep 2012 |

### Fingerprint

### Keywords

- distance-regular graph
- distance matrices
- Eigenvalues
- idempotents
- local spectrum
- predistance polynomials

### Cite this

*Discrete Mathematics*,

*312*(17), 2730-2734. https://doi.org/10.1016/j.disc.2012.03.003

}

*Discrete Mathematics*, vol. 312, no. 17, pp. 2730-2734. https://doi.org/10.1016/j.disc.2012.03.003

**Dual concepts of almost distance-regularity and the spectral excess theorem.** / Dalfo, C.; van Dam, E.R.; Fiol, M.A.; Garriga, E.

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

TY - JOUR

T1 - Dual concepts of almost distance-regularity and the spectral excess theorem

AU - Dalfo, C.

AU - van Dam, E.R.

AU - Fiol, M.A.

AU - Garriga, E.

PY - 2012/9

Y1 - 2012/9

N2 - Generally speaking, ‘almost distance-regular’ graphs share some, but not necessarily all, of the regularity properties that characterize distance-regular graphs. In this paper we propose two new dual concepts of almost distance-regularity, thus giving a better understanding of the properties of distance-regular graphs. More precisely, we characterize m-partially distance-regular graphs and j-punctually eigenspace distance-regular graphs by using their spectra. Our results can also be seen as a generalization of the so-called spectral excess theorem for distance-regular graphs, and they lead to a dual version of it.

AB - Generally speaking, ‘almost distance-regular’ graphs share some, but not necessarily all, of the regularity properties that characterize distance-regular graphs. In this paper we propose two new dual concepts of almost distance-regularity, thus giving a better understanding of the properties of distance-regular graphs. More precisely, we characterize m-partially distance-regular graphs and j-punctually eigenspace distance-regular graphs by using their spectra. Our results can also be seen as a generalization of the so-called spectral excess theorem for distance-regular graphs, and they lead to a dual version of it.

KW - distance-regular graph

KW - distance matrices

KW - Eigenvalues

KW - idempotents

KW - local spectrum

KW - predistance polynomials

U2 - 10.1016/j.disc.2012.03.003

DO - 10.1016/j.disc.2012.03.003

M3 - Article

VL - 312

SP - 2730

EP - 2734

JO - Discrete Mathematics

JF - Discrete Mathematics

SN - 0012-365X

IS - 17

ER -