A quartic graph is a graph which is 4-regular. The unique quartic graph on five nodes is the complete
graph 
,
and the unique quartic graph on six nodes is the octahedral
graph. There are two quartic graphs on seven nodes, one of which is the circulant
graph 
.
A number of the Archimedean solids have skeletons
that are quartic.
The numbers of connected quartic graphs on 
, 2, ... nodes are 0, 0, 0, 0, 1, 1, 2, 6, 16, 59, ... (OEIS
A006820), the numbers of not necessarily connected
quartic graphs are 0, 0, 0, 0, 1, 1, 2, 6, 16, 60, ... (OEIS A033301),
and the numbers of disconnected quartic graphs for 
, 11, ... are 1, 1, 3, 8, 25, 88, ... (OEIS A033483;
Read and Wilson 1998).
The following table gives a list of some named quartic graphs.
| graph | nodes | symmetric |
| pentatope graph | 5 | yes |
| octahedral graph | 6 | yes |
complete
bipartite graph  | 8 | yes |
| (2,4)-rook graph | 8 | no |
generalized quadrangle  | 9 | yes |
| 5-crown graph | 10 | yes |
| 4-Andrásfai graph | 11 | no |
| Chvátal graph | 12 | no |
| cuboctahedral graph | 12 | yes |
| 13-cyclotomic graph | 13 | yes |
| Hoffman graph | 16 | no |
| tesseract graph | 16 | yes |
| Robertson graph | 19 | no |
| Folkman graph | 20 | no |
| Brinkmann graph | 21 | no |
generalized hexagon  | 21 | yes |
| rolling cube graph | 24 | yes |
| small rhombicuboctahedral graph | 24 | no |
| 25-Grünbaum graph 25 | 25 | no |
| (4,6)-cage graph | 26 | yes |
| Doyle graph | 27 | yes |
| icosidodecahedral graph | 30 | yes |
| 4-odd graph | 35 | yes |
generalized
octagon  | 45 | yes |
| Harborth graph | 52 | no |
| small rhombicosidodecahedral graph | 60 | no |
| (8,8)-fiveleaper graph | 64 | no |
| (4,7)-cage graph | 67 | no |
| Meredith graph | 70 | no |
| (7,3)-bipartite Kneser graph | 70 | yes |
| (4,8)-cage graph | 80 | no |
| 5-permutation star graph | 120 | yes |
generalized dodecagon  | 189 | no |
| 120-cell graph | 600 | yes |
