16 citations · 77 across the 45 of their papers we have counts for
37 papers · 1 filter
On transitive permutation groups with exponential graph growth
Đorđe Mitrović, Gabriel Verret
Let be a finite connected graph and a vertex-transitive group of its automorphisms. The pair is said to be locally- if the permutation group induced by the acti…
Detecting Graphical and Digraphical Regular Representations in groups of squarefree order
Joy Morris, Gabriel Verret
A necessary condition for a Cayley digraph Cay to be a regular representation is that there are no non-trivial group automorphisms of that fix setwise. A group is DR…
Extremely primitive groups and linear spaces
Melissa Lee, Gabriel Verret
A finite non-regular primitive permutation group is extremely primitive if a point stabiliser acts primitively on each of its nontrivial orbits. Such groups have been studied f…
On orders of automorphisms of vertex-transitive graphs
Primoz Potocnik, Micael Toledo, Gabriel Verret
In this paper we investigate orders, longest cycles and the number of cycles of automorphisms of finite vertex-transitive graphs. In particular, we show that the order of every aut…
Oriented regular representations of out-valency two for finite simple groups
Gabriel Verret, Binzhou Xia
In this paper, we show that every finite simple group of order at least admits an oriented regular representation of out-valency .
Groups for which it is easy to detect graphical regular representations
Dave Witte Morris, Joy Morris, Gabriel Verret
We say that a finite group G is "DRR-detecting" if, for every subset S of G, either the Cayley digraph Cay(G,S) is a digraphical regular representation (that is, its automorphism g…