3 problems

Baker–Ebert–Hemmeter–Woldar's second-largest-clique conjecture. The clique produced by this construction is a second largest maximal clique; equivalently, there is no maximal cliqu…

Fix an integer $d\ge 2$. For each odd prime power q\equiv1{\ifmmode\text{\rm\ (mod~d)}\else\discretionary{}{}{\text{ }}\rm(mod~d)\fi}, let $r_q$ be the cardinality of a maxim…

Let $q$ be an odd prime power, let $d\rvert(q+1)$ with $d e 2$, and let $uinmathbb{F}{q^2}setminusmathbb{F}q$. In $GP(q^2,d)$, let $N(u)$ be the $mathbb{F}q$-neighborhood of $u$, a…