## Incidence graph of $\mathrm{STD}_3[9;3]$

This is the unique such graph which is distance-transitive. There are other examples: the corresponding designs were classified by V. Mavron and V. Tonchev (*Journal of Geometry* **67** (2000), 180–187). These graphs will (hopefully!) be added to this site in the near future.

Number of vertices: | $54$ |

Diameter: | $4$ |

Intersection array: | $\{9,8,6,1;1,3,8,9\}$ |

Spectrum: | $9^1 3^{18} 0^{16} (-3)^{18} (-9)^1$ |

Automorphism group: | order $2^6.3^6$ |

Distance-transitive: | Yes |

Bipartite, Antipodal |