Luke Morgan

activity

20142025

most citedElusive groups of automorphisms of digraphs of small valency

13 citations · 42 across the 22 of their papers we have counts for

collaborators

Showing 2017Show all

5 papers · 1 filter

math.CO2017

Arc-transitive digraphs of given out-valency and with blocks of given size

Luke Morgan, Primoz Potocnik, Gabriel Verret

Given integers $k$ and $m$ , we construct a $G$ -arc-transitive graph of valency $k$ and an $L$ -arc-transitive oriented digraph of out-valency $k$ such that $G$ and $L$ both admit bl…

math.GR2017★ 1 cited

On $p$ -groups with automorphism groups related to the Chevalley group $G_{2} (p)$

John Bamberg, Saul D. Freedman, Luke Morgan

Let $p$ be an odd prime. We construct a $p$ -group $P$ of nilpotency class two, rank seven and exponent $p$ , such that $Aut (P)$ induces $N_{\mathrm{GL}(7,p)}(G_2(p)) = Z(\m…

math.GR2017

A finite simple group is CCA if and only if it has no element of order four

Luke Morgan, Joy Morris, Gabriel Verret

A Cayley graph for a group $G$ is CCA if every automorphism of the graph that preserves the edge-orbits under the regular representation of $G$ is an element of the normaliser of $…

math.CO2017

Digraphs with small automorphism groups that are Cayley on two nonisomorphic groups

Luke Morgan, Joy Morris, Gabriel Verret

Let $Γ = Cay (G, S)$ be a Cayley digraph on a group $G$ and let $A = Aut (Γ)$ . The Cayley index of $Γ$ is $∣ A : G ∣$ . It has previously been shown that, if $p$ is a prime,…

math.CO2017

Characterising CCA Sylow cyclic groups whose order is not divisible by four

Luke Morgan, Joy Morris, Gabriel Verret

A Cayley graph on a group $G$ has a natural edge-colouring. We say that such a graph is CCA if every automorphism of the graph that preserves this edge-colouring is an element of t…

Arc-transitive digraphs of given out-valency and with blocks of given size

On p-groups with automorphism groups related to the Chevalley group G2​(p)

A finite simple group is CCA if and only if it has no element of order four

Digraphs with small automorphism groups that are Cayley on two nonisomorphic groups

Characterising CCA Sylow cyclic groups whose order is not divisible by four

On $p$ -groups with automorphism groups related to the Chevalley group $G_{2} (p)$