**Graph** | **No. of vertices** | **Diameter** |

Octahedron $J(4,2)$ | 6 | 2 |

3-Cube $Q_3 \cong K_{4,4}-I \cong H(3,2)$ | 8 | 3 |

Paley graph $P_9 \cong H(2,3)$ | 9 | 2 |

Petersen graph $O_3 \cong K(5,2)$ | 10 | 2 |

$J(5,2)$ | 10 | 2 |

$K_{5,5}-I$ | 10 | 3 |

Icosahedron | 12 | 3 |

$K_{6,6}-I$ | 12 | 3 |

Paley graph $P_{13}$ | 13 | 2 |

Heawood graph $\cong$ Incidence graph of $PG(2,2)$ | 14 | 3 |

Distance-3 graph of Heawood graph | 14 | 3 |

$K_{7,7}-I$ | 14 | 3 |

Line graph of Petersen graph | 15 | 3 |

$K(6,2)$ | 15 | 2 |

$J(6,2)$ | 15 | 2 |

4-cube $Q_4 \cong H(4,2)$ | 16 | 4 |

$H(2,4)$ | 16 | 2 |

Complement of $H(2,4)$ | 16 | 2 |

Shrikhande graph | 16 | 2 |

Complement of Shrikhande graph | 16 | 2 |

Clebsch graph | 16 | 2 |

Complement of Clebsch graph | 16 | 2 |

$K_{8,8}-I$ | 16 | 2 |

Paley graph $P_{17}$ | 17 | 2 |

Pappus graph | 18 | 4 |

$K_{9,9}-I$ | 18 | 3 |

Dodecahedron | 20 | 5 |

Desargues graph $D(O_3)$ | 20 | 5 |

$J(6,3)$ | 20 | 3 |

$K_{10,10}-I$ | 20 | 3 |

Line graph of Heawood graph | 21 | 3 |

$J(7,2)$ | 21 | 2 |

$K(7,2)$ | 21 | 2 |

Incidence graph of biplane on 11 points | 22 | 3 |

Incidence graph of $(11,6,3)$-design | 22 | 3 |

$K_{11,11}-I$ | 22 | 3 |

Klein graph | 24 | 3 |

$K_{12,12}-I$ | 24 | 3 |

$H(2,5)$ | 25 | 2 |

Paley graph $P_{25}$ | 25 | 2 |

Paulus graphs, $\mathrm{SRG}(25,12,5,6)$ (N=14, 7 pairs) | 25 | 2 |

Complement of $H(2,5)$ | 25 | 2 |

Paulus graphs, $\mathrm{SRG}(26,10,3,4)$ (N=10) | 26 | 2 |

Complements of Paulus graphs, $\mathrm{SRG}(26,15,8,9)$ (N=10) | 26 | 2 |

Incidence graph of $PG(2,3)$ | 26 | 3 |

Incidence graph of $(13,9,3)$-design | 26 | 3 |

$K_{13,13}-I$ | 26 | 3 |

Complements of Paulus graphs, $\mathrm{SRG}(26,15,8,9)$ (N=10) | 26 | 2 |

$H(3,3)$ | 27 | 3 |

$GQ(2,4)$ minus spread (N=2) | 27 | 3 |

Complement of Schläfli graph | 27 | 2 |

Schläfli graph | 27 | 2 |

Coxeter graph | 28 | 4 |

$J(8,2)$ | 28 | 2 |

Chang graphs (N=3) | 28 | 2 |

Taylor graph from $P_{13}$ | 28 | 3 |

$K_{14,14}-I$ | 28 | 3 |

$K(8,2)$ | 28 | 2 |

Complements of Chang graphs (N=3) | 28 | 2 |

Paley graph $P_{29}$ | 29 | 2 |

Other $\mathrm{SRG}(29,14,6,7)$ (N=40, 20 pairs) | 29 | 2 |

Tutte's 8-cage | 30 | 4 |

Incidence graph of $PG(3,2)$ | 30 | 3 |

Incidence graphs of Hadamard $(15,7,3)$-designs (N=4) | 30 | 3 |

Incidence graph of complement of $PG(3,2)$ | 30 | 3 |

Incidence graphs of $(15,8,4)$-designs (N=4) | 30 | 3 |

$K_{15,15}-I$ | 30 | 3 |

Incidence graph of $AG(2,4)$ minus a parallel class | 32 | 4 |

5-cube $Q_5 \cong H(5,2)$ | 32 | 5 |

Armanios-Wells graph | 32 | 4 |

Folded 6-cube | 32 | 3 |

Incidence graphs of biplanes on 16 points (N=3) | 32 | 3 |

Incidence graphs of $(16,10,6)$-designs (N=3) | 32 | 3 |

Hadamard graph on 32 vertices | 32 | 4 |

Taylor graph from $J(6,2) \cong$ Halved 6-cube | 32 | 3 |

Taylor graph from $K(6,2)$ | 32 | 3 |

$K_{16,16}-I$ | 32 | 3 |

$K_{17,17}-I$ | 34 | 3 |

Folded Johnson graph $J(8,4) \cong$ Merged Johnson graph $J(7,3)$ | 35 | 2 |

Grassmann graph $J_2(4,2)$ | 35 | 2 |

Odd graph $O_4$ | 35 | 3 |

$J(7,3)$ | 35 | 3 |

Sylvester graph | 36 | 3 |

Hexacode graph | 36 | 4 |

$H(2,6)$ | 36 | 2 |

Point graphs of $GQ(3,3)$ and its dual | 40 | 2 |

Coolsaet-Degraer 3-cover of $K_{14}$ | 42 | 3 |

Incidence graph of $PG(2,4)$ | 42 | 3 |

Symplectic 3-cover of $K_{14}$ | 42 | 3 |

2^{nd} subconstituent of Hoffman-Singleton graph | 42 | 3 |

Line graph of Tutte's 8-cage | 45 | 4 |

Halved Foster graph | 45 | 4 |

Point graph of $GQ(4,2)$ | 45 | 2 |

Hadamard graph on 48 vertices | 48 | 4 |

$H(2,7)$ | 49 | 2 |

Peisert graph on 49 vertices | 49 | 2 |

Incidence graph of $AG(2,5)$ minus a parallel class | 50 | 4 |

Hoffman-Singleton graph | 50 | 2 |

Complement of Hoffman-Singleton graph | 50 | 2 |