Descriptions of various graphs. A slowly growing collection. See, for example,

The Petersen graph on 10 vertices.

The Heawood graph on 14 vertices.

The Sp(4,2) Generalized Quadrangle on 15 vertices.

The Clebsch graph on 16 vertices.

The Shrikhande graph on 16 vertices.

The Möbius-Kantor graph on 16 vertices.

The Pappus graph on 18 vertices.

The Desargues graph on 20 vertices.

The Dodecahedral (0,2)-graph on 20 vertices.

The Paulus graphs on 25 and 26 vertices.

The Schläfli graph on 27 vertices.

The Chang graphs on 28 vertices.

The Coxeter graph on 28 vertices.

The Folded 6-cube on 32 vertices.

The Armanios-Wells graph on 32 vertices.

The Dyck graph on 32 vertices.

The U3(3).2 graph on 36 vertices.

The Sylvester graph on 36 vertices.

The Hoffman-Singleton graph on 50 vertices.

The Gray graph on 54 vertices.

Representations of PGL(2,11) on 55 vertices.

The Sims-Gewirtz graph on 56 vertices.

The Perkel graph on 57 vertices.

The affine polar graphs on 64 vertices.

The M22 graph on 77 vertices.

The Brouwer-Haemers graph (VO(4,3)) on 81 vertices.

The Higman-Sims graph on 100 vertices.

The Hall-Janko graph on 100 vertices.

The 1st subconstituent of the McLaughlin graph (O(6,3)) on 112 vertices.

The 2nd subconstituent of the McLaughlin graph (U4(3).22) on 162 vertices.

The Cameron graph on 231 vertices.

The McLaughlin graph on 275 vertices.

The Cohen-Tits near octagon on 315 vertices.

The G2(4) graph on 416 vertices.

The Suzuki graph on 1782 vertices.

The Affine orthogonal graphs.

Cages.

cubelike graphs.

cubic distance-regular graphs.

The Grassmann graphs.

The Hamming graphs.

Integral trees.

The Johnson graphs.

Kneser graphs.

For Lattice graphs, see Hamming graphs.

The Odd graphs.

Orthogonal arrays.

Paley graphs.

Polygonal graphs.

Rectagraphs.

Steiner systems.

Steiner triple systems.

Strongly regular graphs and tables of strongly regular graph parameters, and more tables of parameters for some big strongly regular graphs, and for some families.

Symplectic graphs.

For Triangular graphs, see Johnson graphs.

2-graphs.

For (0,2)-graphs, see Rectagraphs.