A noncayley graph is a graph which is not a Cayley graph. All graphs that are not vertex-transitive
are noncayley graphs. However, some vertex-transitive
graphs are noncayley. The numbers of noncayley vertex-transitive
graphs on 
,
2, ... nodes are 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0,
0, 0, 0, 4, 8, 0, 4, 0, 82, ... (OEIS A006792;
McKay and Royle 1990, McKay and Praeger 1994), with the first nonzero case occurring
at 
.
Royle listed noncayley graphs up to 31 vertices. The values for 27, 28, and 30 vertices have not been independently verified. Errors in the group data affect this enumeration only if a minimal transitive group has been omitted.
A partial list of undirected vertex-transitive graphs that are not Cayley graphs is given in the following table (Holton and Sheehan 1993, p. 292). The great rhombicuboctahedral graph and great rhombicosidodecahedral graph are Cayley graphs and are excluded (Scherphuis).
| 10 | 5-triangular graph |
| 10 | Petersen graph |
| 15 | vertex-transitive
graph  |
| 15 | 6-triangular graph |
| 15 |  -generalized quadrangle |
| 15 | quartic vertex-transitive graph Qt39 |
| 16 | quartic vertex-transitive graph Qt44 |
| 20 | 6-tetrahedral Johnson graph |
| 20 | Desargues graph |
| 20 | dodecahedral graph |
| 26 |  -generalized Petersen graph |
| 28 |  -Kneser graph |
| 28 | 8-triangular graph |
| 28 | Coxeter graph |
| 30 |  -arrangement graph |
| 30 | cubic vertex-transitive graph Ct57 |
| 30 | cubic vertex-transitive graph Ct66 |
| 30 | icosidodecahedral graph |
| 30 | Tutte 8-cage |
| 30 | line graph of the icosahedral graph |
| 30 |  -permutation star graph |
| 30 | Kronecker product of Petersen line
graph complement and ones matrix  |
| 84 | triangle-replaced Coxeter graph |
