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papers

Publications (43)

math.GR2021

Orbits of Sylow subgroups of finite permutation groups

John Bamberg, Alexander Bors, Alice Devillers +3

We say that a finite group $G$ acting on a set $I^c ◯$ has Property $(*)_{p}$ for a prime $p$ if $P_{I ¨} $ is a Sylow $p$ -subgroup of $G_{I ¨} $ for all $I ¨ \in I^c ◯$ and Sylow $p$ -subgroups $P$ o…

math.CO2011

A classification of graphs whose subdivision graphs are locally $G$ -distance transitive

Ashraf Daneshkhah, Alice Devillers

The subdivision graph $S (I^£)$ of a connected graph $I^£$ is constructed by adding a vertex in the middle of each edge. In a previous paper written with Cheryl E. Praeger, we charact…

math.CO2007

Primitive decompositions of Johnson graphs

Alice Devillers, Michael Giudici, Cai Heng Li +1

A transitive decomposition of a graph is a partition of the edge set together with a group of automorphisms which transitively permutes the parts. In this paper we determine all tr…

math.CO2020

Delandtsheer--Doyen parameters for block-transitive point-imprimitive 2-designs

Carmen Amarra, Alice Devillers, Cheryl E. Praeger

Delandtsheer and Doyen bounded, in terms of the block size, the number of points of a point-imprimitive, block-transitive 2-design. To do this they introduced two integer parameter…

math.CO2020

On flag-transitive 2-(v,k,2) designs

Alice Devillers, Hongxue Liang, Cheryl E. Praeger +1

This paper is devoted to the classification of flag-transitive 2-(v,k,2) designs. We show that apart from two known symmetric 2-(16,6,2) designs, every flag-transitive subgroup G o…

math.CO2024

Triangle-free graphs with diameter 2

Alice Devillers, Nina KamÄev, Brendan McKay +5

There are finitely many graphs with diameter $2$ and girth 5. What if the girth 5 assumption is relaxed? Apart from stars, are there finitely many triangle-free graphs with diamete…

math.CO2024

Chain-imprimitive, flag-transitive 2-designs

Carmen Amarra, Alice Devillers, Cheryl E. Praeger

We consider $2$ -designs which admit a group of automorphisms that is flag-transitive and leaves invariant a chain of nontrivial point-partitions. We build on our recent work on $2$ …

math.GR2011

An infinite family of biquasiprimitive 2-arc transitive cubic graphs

Alice Devillers, Michael Giudici, Cai Heng Li +1

A new infinite family of bipartite cubic 3-arc transitive graphs is constructed and studied. They provide the first known examples admitting a 2-arc transitive vertex-biquasiprimit…

math.CO2022

Tournaments and Even Graphs are Equinumerous

Gordon F. Royle, Cheryl E. Praeger, S. P. Glasby +2

A graph is called odd if there is an orientation of its edges and an automorphism that reverses the sense of an odd number of its edges, and even otherwise. Pontus von BrÃ¶mssen (n…

math.CO2012

Line graphs and $2$ -geodesic transitivity

Alice Devillers, Wei Jin, Cai Heng Li +1

For a graph $I^$ , a positive integer $s$ and a subgroup $G\leq \Aut(Î)$, we prove that $G$ is transitive on the set of $s$ -arcs of $I^$ if and only if $I^$ has girth at least $2(s…

math.CO2010

Locally $s$ -distance transitive graphs

Alice Devillers, Michael Giudici, Cai Heng Li +1

We give a unified approach to analysing, for each positive integer $s$ , a class of finite connected graphs that contains all the distance transitive graphs as well as the locally $…

math.CO2015

Pairwise transitive 2-designs

Alice Devillers, Cheryl E. Praeger

We classify the pairwise transitive 2-designs, that is, 2-designs such that a group of automorphisms is transitive on the following five sets of ordered pairs: point-pairs, inciden…

math.CO2026

The distinguishing number of complete bipartite and crown graphs

Lei Chen, Alice Devillers, Luke Morgan +1

The distinguishing number of a permutation group $G\leqslant\Sym(Î©)$ is the minimum number of colours needed to colour $I^c ◯$ in such a way that the only colour preserving element o…

math.GR2025

Proper partial linear spaces affording imprimitive rank 3 automorphism groups

Anton A. Baykalov, Alice Devillers, Cheryl E. Praeger

A partial linear space is a point--line incidence structure such that each line is incident with at least two points and each pair of points is incident with at most one line. It i…

math.GR2019

The distinguishing number of quasiprimitive and semiprimitive groups

Alice Devillers, Scott Harper, Luke Morgan

The distinguishing number of $G \leqslant \sym(Î©)$ is the smallest size of a partition of $I^c ◯$ such that only the identity of $G$ fixes all the parts of the partition. Extending e…

math.GR2022

Rank three innately transitive permutation groups and related $2$ -transitive groups

Anton A. Baykalov, Alice Devillers, Cheryl E. Praeger

The sets of primitive, quasiprimitive, and innately transitive permutation groups may each be regarded as the building blocks of finite transitive permutation groups, and are analo…

math.CO2024

Higher-dimensional grid-imprimitive block-transitive designs

Seyed Hassan Alavi, Carmen Amarra, Ashraf Daneshkhah +2

It was shown in 1989 by Delandtsheer and Doyen that, for a $2$ -design with $v$ points and block size $k$ , a block-transitive group of automorphisms can be point-imprimitive (that i…

math.CO2012

Automorphisms and opposition in twin buildings

Alice Devillers, James Parkinson, Hendrik Van Maldeghem

We show that every automorphism of a thick twin building interchanging the halves of the building maps some residue to an opposite one. Furthermore we show that no automorphism of…

math.CO2011

On distance, geodesic and arc transitivity of graphs

Alice Devillers, Wei Jin, Cai Heng Li +1

We compare three transitivity properties of finite graphs, namely, for a positive integer $s$ , $s$ -distance transitivity, $s$ -geodesic transitivity and $s$ -arc transitivity. It is…

math.CO2022

Block-transitive two-designs based on grids

Seyed Hassan Alavi, Ashraf Daneshkhah, Alice Devillers +1

We study point-block incidence structures $(P, B)$ for which the point set $P$ is an $m \times n$ grid. Cameron and the fourth author showed that each b…

math.CO2016

The circular altitude of a graph

John Bamberg, Brian Corr, Alice Devillers +3

In this paper we investigate a parameter of graphs, called the circular altitude, introduced by Peter Cameron. We show that the circular altitude provides a lower bound on the circ…

math.CO2020

On flag-transitive imprimitive 2-designs

Alice Devillers, Cheryl E. Praeger

In 1987, Huw Davies proved that, for a flag-transitive point-imprimitive $2$ - $(v, k, I^»)$ design, both the block-size $k$ and the number $v$ of points are bounded by functions of $Î»…

math.GR2011

Symmetry properties of subdivision graphs

Ashraf Daneshkhah, Alice Devillers, Cheryl E. Praeger

The subdivision graph $S (I^£)$ of a graph $I^£$ is obtained from $I^£$ by `adding a vertex' in the middle of every edge of $\Si$. Various symmetry properties of $A^§ (I^£)$ are studied.…

math.GR2025

Linear dimension of group actions

Alice Devillers, Michael Giudici, Daniel R. Hawtin +2

Two fundamental ways to represent a group are as permutations and as matrices. In this paper, we study linear representations of groups that intertwine with a permutation represent…

math.CO2015

Finite 2-geodesic transitive graphs of prime valency

Alice Devillers, Wei Jin, Cai Heng Li +1

We classify non-complete prime valency graphs satisfying the property that their automorphism group is transitive on both the set of arcs and the set of $2$ -geodesics. We prove tha…

math.GR2025

Block-transitive designs with a poset of imprimitive partitions

Carmen Amarra, Alice Devillers, Cheryl E. Praeger

We study block designs which admit an automorphism group that is transitive on blocks and points, and leaves invariant every partition in a given finite poset of partitions of the…

math.CO2022

Analysing flag-transitive point-imprimitive 2-designs

Alice Devillers, Cheryl E. Praeger

In this paper we develop several general methods for analysing flag-transitive point-imprimitive $2$ -designs, which give restrictions on both the automorphisms and parameters of su…

math.GR2021

Partial linear spaces with a rank 3 affine primitive group of automorphisms

John Bamberg, Alice Devillers, Joanna B. Fawcett +1

A partial linear space is a pair $(P, L)$ where $P$ is a non-empty set of points and $L$ is a collection of subsets of $P$ called l…

math.CO2013

Locally s-distance transitive graphs and pairwise transitive designs

Alice Devillers, Michael Giudici, Cai Heng Li +1

The study of locally s-distance transitive graphs initiated by the authors in previous work, identified that graphs with a star quotient are of particular interest. This paper show…

math.CO2026

Recursive constructions for block-transitive, poset-imprimitive two-designs

Carmen Amarra, Alice Devillers, Cheryl E. Praeger

We give two general constructions for $2$ -designs, that can be used recursively, and interchangeably, to produce new infinite families of $2$ -designs admitting block-transitive gro…

math.CO2024

Transitive path decompositions of Cartesian products of complete graphs

Ajani De Vas Gunasekara, Alice Devillers

An $H$ -decomposition of a graph $I^$ is a partition of its edge set into subgraphs isomorphic to $H$ . A transitive decomposition is a special kind of $H$ -decomposition that is high…

math.CO2023

Block-transitive 2-designs with a chain of imprimitive partitions

Carmen Amarra, Alice Devillers, Cheryl E. Praeger

More than $30$ years ago, Delandtsheer and Doyen showed that the automorphism group of a block-transitive $2$ -design, with blocks of size $k$ , could leave invariant a nontrivial po…

math.NT2020

Roots of unity and unreasonable differentiation

Alice Devillers, S. P. Glasby

We explore when it is legal to differentiate a polynomial evaluated at a root of unity using modular arithmetic.

math.GR2014

Locally triangular graphs and rectagraphs with symmetry

John Bamberg, Alice Devillers, Joanna B. Fawcett +1

Locally triangular graphs are known to be halved graphs of bipartite rectagraphs, which are connected triangle-free graphs in which every $2$ -arc lies in a unique quadrangle. A gra…

math.CO2025

Extendibility of Latin Hypercuboids

A Latin hypercuboid of order $n$ is a $d$ -dimensional matrix of dimensions $n \times n \times \dots \times n \times k$ , with symbols from a set of cardinality $n$ such that each symbol…

math.GR2011

Codistances of 3-spherical buildings

Alice Devillers, Bernhard MÃ¼hlherr, Hendrik Van Maldeghem

We show that a 3-spherical building in which each rank 2 residue is connected far away from a chamber, and each rank 3 residue is simply 2-connected far away from a chamber, admits…

math.CO2022

Arc-transitive bicirculants

Alice Devillers, Michael Giudici, Wei Jin

In this paper, we characterise the family of finite arc-transitive bicirculants. We show that every finite arc-transitive bicirculant is a normal $r$ -cover of an arc-transitive gra…

math.GR2011

On imprimitive rank 3 permutation groups

Alice Devillers, Michael Giudici, Cai Heng Li +2

A classification is given of rank 3 group actions which are quasiprimitive but not primitive. There are two infinite families and a finite number of individual imprimitive examples…

math.CO2008

The sphericity of the complex of non-degenerate subspaces

Alice Devillers, Ralf KÃ¶hl, Bernhard Muhlherr

We prove that the complex of proper non-trivial non-degenerate subspaces of a finite-dimensional vector space endowed with a non-degenerate sesquilinear form is homotopy equivalent…

math.GR2022

The groups $G$ satisfying a functional equation $f (x k) = x f (x)$ for some $k \in G$

Dominik Bernhardt, Tim Boykett, Alice Devillers +2

We study the groups $G$ with the curious property that there exists an element $k \in G$ and a function $f : G \to G$ such that $f (x k) = x f (x)$ holds for all $x \in G$ . This propert…

math.CO2011

Quotients of incidence geometries

Philippe Cara, Alice Devillers, Michael Giudici +1

We develop a theory for quotients of geometries and obtain sufficient conditions for the quotient of a geometry to be a geometry. These conditions are compared with earlier work on…

math.GR2020

On $k$ -connected-homogeneous graphs

Alice Devillers, Joanna B. Fawcett, Cheryl E. Praeger +1

A graph $I^$ is $k$ -connected-homogeneous ( $k$ -CH) if $k$ is a positive integer and any isomorphism between connected induced subgraphs of order at most $k$ extends to an automorph…

math.CO2022

Codes and Designs in Johnson Graphs From Symplectic Actions on Quadratic Forms

John Bamberg, Alice Devillers, Mark Ioppolo +1

The Johnson graph $J (v, k)$ has as vertices the $k$ -subsets of $V = {1, \dots, v}$ , and two vertices are joined by an edge if their intersection has size $k - 1$ . An \emph{…

Publications (43)

Orbits of Sylow subgroups of finite permutation groups

A classification of graphs whose subdivision graphs are locally G-distance transitive

Primitive decompositions of Johnson graphs

Delandtsheer--Doyen parameters for block-transitive point-imprimitive 2-designs

On flag-transitive 2-(v,k,2) designs

Triangle-free graphs with diameter 2

Chain-imprimitive, flag-transitive 2-designs

An infinite family of biquasiprimitive 2-arc transitive cubic graphs

Tournaments and Even Graphs are Equinumerous

Line graphs and 2-geodesic transitivity

Locally s-distance transitive graphs

Pairwise transitive 2-designs

The distinguishing number of complete bipartite and crown graphs

Proper partial linear spaces affording imprimitive rank 3 automorphism groups

The distinguishing number of quasiprimitive and semiprimitive groups

Rank three innately transitive permutation groups and related 2-transitive groups

Higher-dimensional grid-imprimitive block-transitive designs

Automorphisms and opposition in twin buildings

On distance, geodesic and arc transitivity of graphs

Block-transitive two-designs based on grids

The circular altitude of a graph

On flag-transitive imprimitive 2-designs

Symmetry properties of subdivision graphs

Linear dimension of group actions

Finite 2-geodesic transitive graphs of prime valency

Block-transitive designs with a poset of imprimitive partitions

Analysing flag-transitive point-imprimitive 2-designs

Partial linear spaces with a rank 3 affine primitive group of automorphisms

Locally s-distance transitive graphs and pairwise transitive designs

Recursive constructions for block-transitive, poset-imprimitive two-designs

Transitive path decompositions of Cartesian products of complete graphs

Block-transitive 2-designs with a chain of imprimitive partitions

Roots of unity and unreasonable differentiation

Locally triangular graphs and rectagraphs with symmetry

Extendibility of Latin Hypercuboids

Codistances of 3-spherical buildings

Arc-transitive bicirculants

On imprimitive rank 3 permutation groups

The sphericity of the complex of non-degenerate subspaces

The groups G satisfying a functional equation f(xk)=xf(x) for some k∈G

Quotients of incidence geometries

On k-connected-homogeneous graphs

Codes and Designs in Johnson Graphs From Symplectic Actions on Quadratic Forms

A classification of graphs whose subdivision graphs are locally $G$ -distance transitive

Line graphs and $2$ -geodesic transitivity

Locally $s$ -distance transitive graphs

Rank three innately transitive permutation groups and related $2$ -transitive groups

The groups $G$ satisfying a functional equation $f (x k) = x f (x)$ for some $k \in G$

On $k$ -connected-homogeneous graphs