Second largest maximal cliques in small Paley graphs of square order

Huye Chen, Sergey Goryainov, Cong Hu

There is a conjecture that the second largest maximal cliques in Paley graphs of square order $P(q^2)$ have size $\frac{q+\epsilon }{2}$, where $q\equiv \epsilon (\mathrm{mod}4)$, and split into two orbi…