## $\text{Zara graph on 126 vertices}$

This is the unique graph on 126 vertices with the properties that (i) any maximal clique has six vertices, and (ii) if $C$ is a maximal clique and $v$ is a vertex outside of $C$, then $v$ has exactly two neighbours in $C$. Uniqueness was shown by Blokhuis and Brouwer (1984). It is a strongly regular graph with parameters $(126,45,12,18)$, but there are other examples of SRGs with these parameters.

 Number of vertices: $126$ Diameter: $2$ Intersection array: $\{45,32;1,18\}$ Spectrum: $45^1 3^{90} (-9)^{35}$ Automorphism group: $PSU(4,3).2^2$ Distance-transitive: $\text{Yes}$ Primitive

## References

Back to: A-Z indexGraphs with 101-150 verticesGraphs with diameter 2
Last updated: 2 July 2017