The automorphism group of the derangement graph of ${\mathrm{PGL}}_2(q)$ acting on the projective line

Andriaherimanana Sarobidy Razafimahatratra

Given a finite transitive group $G\le \mathrm{Sym}(\Omega )$, the derangement graph ${\Gamma }_G$ is the graph whose vertex set is $G$, and two vertices $g$ and $h$ are adjacent if the ra…