5 problems

Let $q>3$ be a prime power, and consider a Peisert graph of order $q^4$ containing the subfield $\mathbb{F}_q$ as a clique. Yip's Peisert graph conjecture. The subfield…

For a prime $p\geq 3$, consider subsets $I\subset\{0,1,\ldots,p\}$ with $0\in I$ and $|I|=(p+1)/2$, and the associated graph $PP(p^4,p+1,I)$. Let $g$ be the primitive element used…

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…