### Abstract

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

Pages (from-to) | 203-222 |

Journal | Ars Mathematica Contemporanea |

Volume | 17 |

Issue number | 1 |

DOIs | |

Publication status | Published - 2019 |

### Fingerprint

### Keywords

- Cayley graph
- distance-regular graph

### Cite this

*Ars Mathematica Contemporanea*,

*17*(1), 203-222. https://doi.org/10.26493/1855-3974.1964.297

}

*Ars Mathematica Contemporanea*, vol. 17, no. 1, pp. 203-222. https://doi.org/10.26493/1855-3974.1964.297

**Distance-regular Cayley graphs with small valency.** / van Dam, Edwin; Jazaeri, Mojtaba.

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

TY - JOUR

T1 - Distance-regular Cayley graphs with small valency

AU - van Dam, Edwin

AU - Jazaeri, Mojtaba

PY - 2019

Y1 - 2019

N2 - We consider the problem of which distance-regular graphs with small valency are Cayley graphs. We determine the distance-regular Cayley graphs with valency at most 4, the Cayley graphs among the distance-regular graphs with known putative intersection arrays for valency 5, and the Cayley graphs among all distance-regular graphs with girth 3 and valency 6 or 7. We obtain that the incidence graphs of Desarguesian affine planes minus a parallel class of lines are Cayley graphs. We show that the incidence graphs of the known generalized hexagons are not Cayley graphs, and neither are some other distance-regular graphs that come from small generalized quadrangles or hexagons. Among some “exceptional” distance-regular graphs with small valency, we find that the Armanios-Wells graph and the Klein graph are Cayley graphs.

AB - We consider the problem of which distance-regular graphs with small valency are Cayley graphs. We determine the distance-regular Cayley graphs with valency at most 4, the Cayley graphs among the distance-regular graphs with known putative intersection arrays for valency 5, and the Cayley graphs among all distance-regular graphs with girth 3 and valency 6 or 7. We obtain that the incidence graphs of Desarguesian affine planes minus a parallel class of lines are Cayley graphs. We show that the incidence graphs of the known generalized hexagons are not Cayley graphs, and neither are some other distance-regular graphs that come from small generalized quadrangles or hexagons. Among some “exceptional” distance-regular graphs with small valency, we find that the Armanios-Wells graph and the Klein graph are Cayley graphs.

KW - Cayley graph

KW - distance-regular graph

U2 - 10.26493/1855-3974.1964.297

DO - 10.26493/1855-3974.1964.297

M3 - Article

VL - 17

SP - 203

EP - 222

JO - Ars Mathematica Contemporanea

JF - Ars Mathematica Contemporanea

SN - 1855-3974

IS - 1

ER -