A quintic graph is a finite simple graph with at least one graph vertex in which every vertex
degree is 5, so it is 5-regular. The only quintic
graph on 
nodes is the complete
graph 
.
By the handshaking lemma, quintic graphs exist
only on even numbers of nodes.
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 | no |
| 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 | yes |
| 6-permutation star graph | 720 | yes |
