6 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 a power of a prime $p$ satisfying $p\equiv 3\pmod 4$ and $q>3$. Let $P_{q^4}^*$ be the Peisert graph of order $q^4$, and regard the subfield $\mathbb{F}_q$ as a subset o…

Let $q$ be a power of a prime $p$ satisfying $p\equiv 3\pmod 4$ and $q>3$. Let $P_{q^4}^*$ be the Peisert graph of order $q^4$, and let $\omega(P_{q^4}^*)$ denote its clique number…

Let $P_q^*$ denote the Peisert graph of order $q$, and let $\omega(P_q^*)$ be its clique number. A quartic order is an order of the form $q^4$. Quartic Peisert extremality conjectu…

Let $d$ be a positive integer greater than $1$. Let $q \equiv 1 \pmod {2d}$ be a power of a prime $p$, and let $r$ be the largest integer such that $d \mid \frac{q-1}{p^r-1}$. The…