6 problems

A transitive permutation group $L$ is graph-restrictive if there exists a constant $c=c(L)$ such that, whenever $G$ is an arc-transitive group of automorphisms of a graph $\Gamma$…

Upper-bound conjecture. The parameter $s$ for a vertex-primitive $s$-arc-transitive digraph is at most $2$.

Weiss's conjecture. There is a function $f$ defined on the positive integers such that, for every such graph and group, and every vertex $v\in V(\Gamma)$,

For a positive integer $k$, a $k$-circulant is a graph whose automorphism group contains a cyclic semiregular subgroup with $k$ orbits on the vertices. A graph is cubic if every ve…

A descendant set is a directed graph satisfying the properties isolated in Amato's work for descendant sets of highly arc transitive digraphs of finite out-valency. Amato's countab…

Let $c>0$. Let ${\mathcal F}_c$ be a finite family of graphs, let $G$ be an almost simple group, and let $\Gamma$ be a connected tetravalent $G$-arc-transitive graph with vertex…