Actually I have two questions.
Suppose a graph $G$ has either a complete subgraph $K_n$ or else its complement $G^c$ has a complete subgraph $K_n$, and let $r(n, n)$ denote its classical Ramsey number.
Is the sequence
$r(3, 3)$, $r(4, 4)$, $r(5, 5)$, ...
of Ramsey numbers $r(n, n)$ monotone nondecreasing as $n\rightarrow\infty$?
Does $|\operatorname{Aut}(K_n)|$ always divide $|\operatorname{Aut}(G)|$ or otherwise does $|\operatorname{Aut}(K_n)|$ divide $|\operatorname{Aut}(G^c)|$?