$\text{Zara graph on 126 vertices}$

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:$126$
Intersection array:$\{45,32;1,18\}$
Spectrum:$45^1 3^{90} (-9)^{35}$
Automorphism group:$PSU(4,3).2^2$



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Last updated: 2 July 2017