# List of graphs by edges and vertices

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 69 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

1. ^ R. Diestel, Graph Theory, p.8. 3rd Edition, Springer-Verlag, 2005