Second largest maximal cliques in small Paley graphs of square order
Second largest maximal cliques in small Paley graphs of square order
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 $q \equiv \epsilon \pmod 4$, and split into two orbits under the full group of automorphisms whenever $q \ge 25$ (a symmetric description for these two orbits is known). …