Proof of a conjecture on monomial graphs

Xiang-dong Hou, Stephen D. Lappano, Felix Lazebnik

Let $e$ be a positive integer, $p$ be an odd prime, $q=p^e$, and ${\mathbb{F}}_q$ be the finite field of $q$ elements. Let $f,g\in {\mathbb{F}}_q[X,Y]$. The graph $G=G_q(f,g)$ is a biparti…