This graph is the unique $\mathrm{SRG}(21,10,3,6)$. It is the complement of the Johnson graph $\mathrm{J}(7,2)$. It is one of three locally Petersen graphs (Hall 1980).
| Number of vertices: | $21$ |
| Diameter: | $2$ |
| Intersection array: | $\{10,6;1,6\}$ |
| Spectrum: | $10^1 1^{14} (-4)^6$ |
| Automorphism group: | $\mathrm{S}_7$ |
| Distance-transitive: | Yes |
| Primitive |