A cubic vertex-transitive graph is a cubic graph that is vertex transitive. Read and Wilson
(1998, pp. 161-163) enumerate all connected cubic vertex-transitive graphs on
34 and fewer nodes, some of which are illustrated above. The numbers of such graphs
on 
,
4, 6, ... nodes are 0, 1, 2, 2, 3, 4, 3, 4, 5, 7, 3, 11, 5, 6, 10, 10, 5, ... (OEIS
A032355).
The cubic symmetric graphs are a special case of the cubic vertex-transitive graphs (i.e., those that are also edge-transitive).
Classes of connected cubic vertex-transitive graphs include the prism graphs, even Möbius ladders, and crossed prism graphs. Specific cases are summarized in the following table.
| vertices | id | graph |
| 4 | Ct1 | tetrahedral graph |
| 8 | Ct5 | cubical graph |
| 10 | Ct8 | Petersen graph |
| 12 | Ct11 | truncated tetrahedral graph |
| 12 | Ct12 | Franklin graph |
| 14 | Ct15 | Heawood graph |
| 18 | Ct24 | Pappus graph |
| 20 | Ct26 | Desargues graph |
| 20 | Ct27 | dodecahedral graph |
| 24 | Ct39 | cubic symmetric graph  |
| 24 | Ct40 | truncated octahedral graph |
| 24 | Ct45 | truncated cubical graph |
| 28 | Ct53 | Coxeter graph |
| 30 | Ct63 | Tutte 8-cage |
| 32 | Ct71 | Dyck graph |
