Gabriel Verret

activity

20102013

most citedBounding the order of the vertex-stabiliser in 3-valent vertex-transitive and 4-valent arc-transitive graphs

9 citations · 19 across the 8 of their papers we have counts for

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8 papers · 1 filter

math.CO2013★ 1 cited

Arc-transitive graphs of valency 8 have a semiregular automorphism

Gabriel Verret

One version of the polycirculant conjecture states that every vertex-transitive graph has a semiregular automorphism. We give a proof of the conjecture in the arc-transitive case f…

math.CO2012

On intransitive graph-restrictive permutation groups

Pablo Spiga, Gabriel Verret

Let $Γ$ be a finite connected $G$ -vertex-transitive graph and let $v$ be a vertex of $Γ$ . If the permutation group induced by the action of the vertex-stabiliser $G_{v}$ on the neigh…

math.CO2012★ 5 cited

Asymptotic enumeration of vertex-transitive graphs of fixed valency

Primoz Potocnik, Pablo Spiga, Gabriel Verret

Let $G$ be a group and let $S$ be an inverse-closed and identity-free generating set of $G$ . The \emph{Cayley graph} $\Cay(G,S)$ has vertex-set $G$ and two vertices $u$ and $v$ are…

math.CO2012

On the order of arc-stabilisers in arc-transitive graphs with prescribed local group

Primoz Potocnik, Pablo Spiga, Gabriel Verret

Let $Γ$ be a connected $G$ -arc-transitive graph, let $uv$ be an arc of $Γ$ and let $L$ be the permutation group induced by the action of the vertex-stabiliser $G_{v}$ on the neighbou…

math.CO2011★ 1 cited

Bounding the size of a vertex-stabiliser in a finite vertex-transitive graph

Cheryl E. Praeger, Pablo Spiga, Gabriel Verret

In this paper we discuss a method for bounding the size of the stabiliser of a vertex in a $G$ -vertex-transitive graph $Γ$ . In the main result the group $G$ is quasiprimitive or bi…

math.CO2011★ 1 cited

On graph-restrictive permutation groups

Primoz Potocnik, Pablo Spiga, Gabriel Verret

Let $Γ$ be a connected $G$ -vertex-transitive graph, let $v$ be a vertex of $Γ$ and let $L = G_{v}^{Γ (v)}$ be the permutation group induced by the action of the vertex-stabiliser $G_{v}$ …