### Abstract

Language | English |
---|---|

Pages | 2432-2436 |

Number of pages | 5 |

Journal | Discrete Mathematics |

Volume | 340 |

Issue number | 10 |

Early online date | 24 Jun 2017 |

DOIs | |

Publication status | Published - 1 Oct 2017 |

### Fingerprint

### Keywords

- Cayley graphs
- degree–diameter problem
- butterfly networks
- Moore bound

### Cite this

*Discrete Mathematics*,

*340*(10), 2432-2436. https://doi.org/10.1016/j.disc.2017.05.012

}

*Discrete Mathematics*, vol. 340, no. 10, pp. 2432-2436. https://doi.org/10.1016/j.disc.2017.05.012

**Large butterfly Cayley graphs and digraphs.** / Bevan, David.

Research output: Contribution to journal › Article

TY - JOUR

T1 - Large butterfly Cayley graphs and digraphs

AU - Bevan, David

PY - 2017/10/1

Y1 - 2017/10/1

N2 - We present families of large undirected and directed Cayley graphs whose construction is related to butterfly networks. One approach yields, for every large k and for values of d taken from a large interval, the largest known Cayley graphs and digraphs of diameter k and degree d. Another method yields, for sufficiently large k and infinitely many values of d, Cayley graphs and digraphs of diameter k and degree d whose order is exponentially larger in k than any previously constructed. In the directed case, these are within a linear factor in k of the Moore bound.

AB - We present families of large undirected and directed Cayley graphs whose construction is related to butterfly networks. One approach yields, for every large k and for values of d taken from a large interval, the largest known Cayley graphs and digraphs of diameter k and degree d. Another method yields, for sufficiently large k and infinitely many values of d, Cayley graphs and digraphs of diameter k and degree d whose order is exponentially larger in k than any previously constructed. In the directed case, these are within a linear factor in k of the Moore bound.

KW - Cayley graphs

KW - degree–diameter problem

KW - butterfly networks

KW - Moore bound

UR - http://www.sciencedirect.com/science/journal/aip/0012365X

U2 - 10.1016/j.disc.2017.05.012

DO - 10.1016/j.disc.2017.05.012

M3 - Article

VL - 340

SP - 2432

EP - 2436

JO - Discrete Mathematics

T2 - Discrete Mathematics

JF - Discrete Mathematics

SN - 0012-365X

IS - 10

ER -