The Zara graph is the unique graph on 126 vertices satisfying the properties that 1) every maximal clique
(of which there are a total of 567) has six vertices,
and 2) that if 
is a maximal clique and 
is a vertex outside of 
, then 
has exactly two neighbors
in 
(Blokhuis and Brouwer 1984).
The graph is strongly regular with parameters 
,
though it is not the unique graph having such parameters.
It is also both distance-regular with intersection array 
and distance-transitive.
It has graph spectrum 
and is therefore an integral
graph. It has graph automorphism group group order 
.
It is a Hamiltonian graph.
The Zara graph is implemented in the Wolfram Language as GraphData["ZaraGraph"].
