This graph is the complement of the Johnson graph $\mathrm{J}(11,2)$.
| Number of vertices: | $55$ |
| Diameter: | $2$ |
| Intersection array: | $\{36,14;1,28\}$ |
| Spectrum: | $36^1 1^{44} (-8)^{10}$ |
| Automorphism group: | $\mathrm{S}_{11}$ |
| Distance-transitive: | Yes |
| Primitive |