The Cossidente-Penttila graphs are a family of strongly regular graphs with parameters 
for 
an odd prime power. For each such 
, the points of the 
-generalized quadrangle 
can be partitioned into two parts such that the induced subgraph of the point graph
of the generalized quadrangle has the above
parameters on any of them.
Cossidente-Penttila graphs are defined for odd prime powers greater than 1, namely 
, 5, 7, 9, 11, 13, 17, 19, 23, 25, 27, 29, 31, 37, 41, ...
(OEIS A061345), and vertex counts 
.
The smallest Cossidente-Penttila graph corresponds to 
and is isomorphic to the Gewirtz
graph.
