A quintic graph is a graph which is 5-regular. The only quintic graph on nodes is the complete graph . Quintic graphs exist only on even numbers of nodes, and the numbers of connected quintic graphs on , 4, 6, ... nodes are 0, 0, 1, 3, 60, 7848, 3459383, 2585136675, ... (OEIS A006821).
The following table gives some named quintic graphs.
graph | nodes | symmetric |
complete graph | 6 | yes |
(5,3)-cone graph | 8 | no |
complete bipartite graph | 10 | yes |
icosahedral graph | 12 | yes |
6-crown graph | 12 | yes |
5-Andrásfai graph | 14 | yes |
Clebsch graph | 16 | yes |
graph Cartesian product | 18 | no |
(11,5,2)-Levi graph | 22 | yes |
snub cubical graph | 24 | no |
Foster cage | 30 | no |
Meringer graph | 30 | no |
Robertson-Wegner graph | 30 | no |
Wong graph | 30 | no |
Wells graph | 32 | yes |
hypercube graph | 32 | yes |
Sylvester graph | 36 | yes |
(5,6)-cage graph | 42 | yes |
snub dodecahedral graph | 60 | no |
5-odd graph | 126 | yes |
(5,8)-cage graph | 170 | ? |
6-permutation star graph | 720 | yes |