3 problems

Let $q$ be an odd prime power and let $m\geq 2$ divide $q+1$. The $Q_0$-construction and the $\alpha Q_0$-construction produce cliques in the generalised Paley graph…

Let $q$ be an odd prime power, let $m\geq 2$ satisfy $m\mid (q+1)/2$, and consider the cliques in $\mathrm{GP}(q^2,m)$ produced by the $(\mathbb F_q,\alpha)$-construction and the…

Let $q$ be an odd prime power, let $m$ divide $q+1$ with $m\geq 3$, and let $C$ be a clique in the generalised Paley graph $\mathrm{GP}(q^2,m)$ containing $0$ and $1$. The known st…