List of graphs by edges and vertices
From HandWiki
This sortable list points to the articles describing various individual (finite) graphs.[1] 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 |
References
- ↑ R. Diestel, Graph Theory, p.8. 3rd Edition, Springer-Verlag, 2005
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