# List of graphs by edges and vertices

This sortable list points to the articles describing various individual (finite) graphs. The columns 'vertices', 'edges', 'radius', 'diameter', 'girth', 'P' (whether the graph is planar), χ (chromatic number) and χ' (chromatic index) are also sortable, allowing to search for a parameter or another.
See also Graph theory for the general theory, as well as Gallery of named graphs for a list with illustrations.

## List

| name | vertices | edges | radius | diam. | girth | P | χ | χ' |
| 120-cell | 600 | 1200 | 15 | 15 | 5 | F | 3 | 4 |
| Balaban 3-10-cage | 70 | 105 | 6 | 6 | 10 | F | 2 | 3 |
| Balaban 3-11-cage | 112 | 168 | 6 | 8 | 11 | F | 3 | 3 |
| Barnette–Bosák–Lederberg graph | 38 | 57 | 5 | 9 | 4 | T | 3 | 3 |
| Bidiakis cube | 12 | 18 | 3 | 3 | 4 | T | 3 | 3 |
| Biggs–Smith graph | 102 | 153 | 7 | 7 | 9 | F | 3 | 3 |
| Blanuša snarks | 18 | 27 | 4 | 4 | 5 | F | 3 | 4 |
| Brinkmann graph | 21 | 42 | 3 | 3 | 5 | T | 4 | 5 |
| Brouwer–Haemers graph | 81 | 810 | 2 | 2 | 3 | F | 7 | 21 |
| Bull graph | 5 | 5 | 2 | 3 | 3 | T | 3 | 3 |
| Butterfly graph | 5 | 6 | 1 | 2 | 3 | T | 3 | 4 |
| Cameron graph | 231 | 3465 | 2 | 2 | 3 | F | N/A | N/A |
| Chang graphs | 28 | 168 | 2 | 2 | 3 | F | 7 | 12 |
| Chvátal graph | 12 | 24 | 2 | 2 | 4 | F | 4 | 4 |
| Clebsch graph | 16 | 40 | 2 | 2 | 4 | F | 4 | 5 |
| Coxeter graph | 28 | 42 | 4 | 4 | 7 | F | 3 | 3 |
| Cubical graph | 8 | 12 | 3 | 3 | 4 | T | 2 | 3 |
| Cuboctahedral graph | 12 | 24 | 3 | 3 | 3 | T | 3 | 4 |
| Dejter graph | 112 | 336 | 7 | 7 | 6 | F | 2 | 6 |
| Desargues graph | 20 | 30 | 5 | 5 | 6 | F | 2 | 3 |
| Descartes snark | 210 | 315 | N/A | N/A | 5 | N/A | N/A | 4 |
| Diamond graph | 4 | 5 | 1 | 2 | 3 | T | 3 | 3 |
| Dodecahedral graph (20-fullerene) | 20 | 30 | 5 | 5 | 5 | T | 3 | 3 |
| Double-star snark | 30 | 45 | 4 | 4 | 6 | F | 3 | 4 |
| Dürer graph | 12 | 18 | 3 | 4 | 3 | T | 3 | 3 |
| Dyck graph | 32 | 48 | 5 | 5 | 6 | F | 2 | 3 |
| Ellingham–Horton 54-graph | 54 | 81 | 9 | 10 | 6 | F | 2 | 3 |
| Ellingham–Horton 78-graph | 78 | 117 | 7 | 13 | 6 | F | 2 | 3 |
| Errera graph | 17 | 45 | 3 | 4 | 3 | T | 4 | 6 |
| F26A graph | 26 | 39 | 5 | 5 | 6 | F | 2 | 3 |
| Flower snark J(5) | 20 | 30 | 4 | 4 | 5 | F | 3 | 4 |
| Folkman graph | 20 | 40 | 3 | 4 | 4 | F | 2 | 4 |
| Foster 5-5-cage | 30 | 75 | 3 | 3 | 5 | F | 4 | 5 |
| Foster graph | 90 | 135 | 8 | 8 | 10 | F | 2 | 3 |
| Franklin graph | 12 | 18 | 3 | 3 | 4 | F | 2 | 3 |
| Fritsch graph | 9 | 21 | 2 | 2 | 3 | T | 4 | 6 |
| Frucht graph | 12 | 18 | 3 | 4 | 3 | T | 3 | 3 |
| Gewirtz graph | 56 | 280 | 2 | 2 | 4 | F | 4 | 10 |
| 26-fullerene graph (26-fullerene) | 26 | 39 | 5 | 6 | 5 | T | 3 | 3 |
| Goldner–Harary graph | 11 | 27 | 2 | 2 | 3 | T | 4 | 8 |
| Golomb graph | 10 | 18 | 2 | 3 | 3 | T | 4 | 6 |
| Gosset graph | 56 | 756 | 3 | 3 | 3 | F | 14 | 27 |
| Gray graph | 54 | 81 | 6 | 6 | 8 | F | 2 | 3 |
| Grötzsch graph | 11 | 20 | 2 | 2 | 4 | F | 4 | 5 |
| Hall–Janko graph | 100 | 1800 | 2 | 2 | 3 | F | 10 | 36 |
| Harborth graph | 52 | 104 | 6 | 9 | 3 | T | 3 | 4 |
| Harries graph | 70 | 105 | 6 | 6 | 10 | F | 2 | 3 |
| Harries–Wong graph | 70 | 105 | 6 | 6 | 10 | F | 2 | 3 |
| Heawood 3-6-cage graph | 14 | 21 | 3 | 3 | 6 | F | 2 | 3 |
| Herschel graph | 11 | 18 | 3 | 4 | 4 | T | 2 | 4 |
| Hexagonal truncated trapezohedron (24-fullerene) | 24 | 36 | 5 | 5 | 5 | T | 3 | 3 |
| Higman–Sims graph | 100 | 1100 | 2 | 2 | 4 | F | 6 | 22 |
| Hoffman graph | 16 | 32 | 3 | 4 | 4 | F | 2 | 4 |
| Hoffman–Singleton 7-5-cage graph | 50 | 175 | 2 | 2 | 5 | F | 4 | 7 |
| Holt graph | 27 | 54 | 3 | 3 | 5 | F | 3 | 5 |
| Horton graph | 96 | 144 | 10 | 10 | 6 | F | 2 | 3 |
| Icosahedral graph | 12 | 30 | 3 | 3 | 3 | T | 4 | 5 |
| Icosidodecahedral graph | 30 | 60 | 5 | 5 | 3 | T | 3 | 4 |
| Iofinova-Ivanov-110-vertex graph | 110 | 165 | 7 | 7 | 10 | F | 2 | 3 |
| Kittell graph | 23 | 63 | 3 | 4 | 3 | T | 4 | 7 |
| Klein graph (cubic) | 56 | 84 | 6 | 6 | 7 | F | 3 | 3 |
| Klein graph (7-valent) | 24 | 84 | 3 | 3 | 3 | F | 4 | 7 |
| Krackhardt kite graph | 10 | 18 | 2 | 4 | 3 | T | 4 | 6 |
| Livingstone graph | 266 | 1463 | 4 | 4 | 5 | F | N/A | 11 |
| Ljubljana graph | 112 | 168 | 7 | 8 | 10 | F | 2 | 3 |
| Loupekine snark (first) | 22 | 33 | 3 | 4 | 5 | F | 3 | 4 |
| Loupekine snark (second) | 22 | 33 | 3 | 4 | 5 | F | 3 | 4 |
| Markström graph | 24 | 36 | 5 | 6 | 3 | T | 3 | 3 |
| McGee graph | 24 | 36 | 4 | 4 | 7 | F | 3 | 3 |
| McLaughlin graph | 275 | 15400 | 2 | 2 | 3 | F | N/A | 113 |
| Meredith graph | 70 | 140 | 7 | 8 | 4 | F | 3 | 5 |
| Meringer 5-5-cage graph | 30 | 75 | 3 | 3 | 5 | F | 3 | 5 |
| Möbius–Kantor graph | 16 | 24 | 4 | 4 | 6 | F | 2 | 3 |
| Moser spindle | 7 | 11 | 2 | 2 | 3 | T | 4 | 4 |
| Nauru graph | 24 | 36 | 4 | 4 | 6 | F | 2 | 3 |
| Null graph | 0 | 0 | 0 | 0 | N/A | T | 0 | 0 |
| Octahedral graph | 6 | 12 | 2 | 2 | 3 | T | 3 | 4 |
| Paley graph of order 13 | 13 | 39 | 2 | 2 | 3 | F | 5 | 7 |
| Pappus graph | 18 | 27 | 4 | 4 | 6 | F | 2 | 3 |
| Perkel graph | 57 | 171 | 3 | 3 | 5 | F | 3 | 7 |
| Petersen 3-5-cage graph | 10 | 15 | 2 | 2 | 5 | F | 3 | 4 |
| Poussin graph | 15 | 39 | 3 | 3 | 3 | T | 4 | 6 |
| Rhombicosidodecahedral graph | 60 | 120 | 8 | 8 | 3 | T | 3 | 4 |
| Rhombicuboctahedral graph | 24 | 48 | 5 | 5 | 3 | T | 3 | 4 |
| Robertson 4-5-cage graph | 19 | 38 | 3 | 3 | 5 | F | 3 | 5 |
| Robertson–Wegner 5-5-cage graph | 30 | 75 | 3 | 3 | 5 | F | 4 | 5 |
| Schläfli graph | 27 | 216 | 2 | 2 | 3 | F | 9 | 17 |
| Shrikhande graph | 16 | 48 | 2 | 2 | 3 | F | 4 | 6 |
| Snub cubical graph | 24 | 60 | 4 | 4 | 3 | T | 3 | 5 |
| Snub dodecahedral graph | 60 | 150 | 7 | 7 | 3 | T | 4 | 5 |
| Sousselier graph | 16 | 27 | 2 | 3 | 5 | F | 3 | 5 |
| Sylvester graph | 36 | 90 | 3 | 3 | 5 | F | 4 | 5 |
| Szekeres snark | 50 | 75 | 6 | 7 | 5 | F | 3 | 4 |
| Tetrahedral graph | 4 | 6 | 1 | 1 | 3 | T | 4 | 3 |
| Thomsen graph | 6 | 9 | 2 | 2 | 4 | F | 2 | 3 |
| Tietze's graph | 12 | 18 | 3 | 3 | 3 | F | 3 | 4 |
| Triangle graph | 3 | 3 | 1 | 1 | 3 | T | 3 | 3 |
| Truncated cubical graph | 24 | 36 | 6 | 6 | 3 | T | 3 | 3 |
| Truncated cuboctahedral graph | 48 | 72 | 9 | 9 | 4 | T | 2 | 3 |
| Truncated dodecahedral graph | 60 | 90 | 10 | 10 | 3 | T | 3 | 3 |
| Truncated icosahedral graph (60-fullerene) | 60 | 90 | 9 | 9 | 5 | T | 3 | 3 |
| Truncated icosidodecahedral graph | 120 | 180 | 15 | 15 | 4 | T | 2 | 3 |
| Truncated octahedral graph | 24 | 36 | 6 | 6 | 4 | T | 2 | 3 |
| Truncated tetrahedral graph | 12 | 18 | 3 | 3 | 3 | T | 3 | 3 |
| Tutte 3-12-cage | 126 | 189 | 6 | 6 | 12 | F | 2 | 3 |
| Tutte graph | 46 | 69 | 5 | 8 | 4 | T | 3 | 3 |
| Tutte 3-8-cage graph | 30 | 45 | 4 | 4 | 8 | F | 2 | 3 |
| Wagner graph | 8 | 12 | 2 | 2 | 4 | F | 3 | 3 |
| Watkins snark | 50 | 75 | 7 | 7 | 5 | F | 3 | 4 |
| Wells graph | 32 | 80 | 4 | 4 | 5 | F | 4 | 5 |
| Wiener–Araya graph | 42 | 67 | 5 | 7 | 4 | T | 3 | 4 |
| Wong 5-5-cage graph | 30 | 75 | 3 | 3 | 5 | F | 4 | 5 |