Daniel R. Hawtin

activity

20122026

most citedThe circular altitude of a graph

1 citations · 1 across the 16 of their papers we have counts for

collaborators

19 papers

math.CO2026

Symmetries of regular $q$ -graphs

Daniel R Hawtin, Padraig Ó Catháin

Given a finite vector space $V = F_{q}^{n}$ , the $q$ -analogue of a graph, called a $q$ -graph, is a pair $Γ = (V, E)$ , where $V$ is the set of $1$ -dime…

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.CO2024

Alphabet-affine 2-neighbour-transitive codes

Daniel R. Hawtin

A code $C$ is a subset of the vertex set of a Hamming graph $H (n, q)$ , and $C$ is $2$ -neighbour-transitive if the automorphism group $G={\rm Aut}({\mathcal C})…

math.CO2024

Group actions on codes in graphs

Daniel R. Hawtin, Cheryl E. Praeger

This is a chapter in a forthcoming book on completely regular codes in distance regular graphs. The chapter provides an overview, and some original results, on codes in distance re…

math.CO2024

Transitive $(q - 1)$ -fold packings of $PG_{n} (q)$

Daniel R. Hawtin

A $t$ -fold packing of a projective space $PG_{n} (q)$ is a collection $P$ of line-spreads such that each line of $PG_{n} (q)$ occurs in precisely $t$ spreads in $\mat…

math.CO2023

An explicit construction for large sets of infinite dimensional $q$ -Steiner systems

Daniel R. Hawtin

Let $V$ be a vector space over the finite field $F_{q}$ . A $q$ -Steiner system, or an $S (t, k, V)_{q}$ , is a collection $B$ of $k$ -dimensional subspaces of $V$ such t…

math.CO2023

Neighbour-transitive codes in Kneser graphs

Dean Crnković, Daniel R. Hawtin, Nina Mostarac +1

A code $C$ is a subset of the vertex set of a graph and $C$ is $s$ -neighbour-transitive if its automorphism group $Aut (C)$ acts transitively on each of the first $s + 1$ parts…

math.CO2023

Using mixed dihedral groups to construct normal Cayley graphs, and a new bipartite $2$ -arc-transitive graph which is not a Cayley graph

Daniel R. Hawtin, Cheryl E. Praeger, Jin-Xin Zhou

A \emph{mixed dihedral group} is a group $H$ with two disjoint subgroups $X$ and $Y$ , each elementary abelian of order $2^{n}$ , such that $H$ is generated by $X \cup Y$ , and $H/H'\con…

math.CO2023

A family of $2$ -groups and an associated family of semisymmetric, locally $2$ -arc-transitive graphs

Daniel R. Hawtin, Jin-Xin Zhou, Cheryl E. Praeger

A mixed dihedral group is a group $H$ with two disjoint subgroups $X$ and $Y$ , each elementary abelian of order $2^{n}$ , such that $H$ is generated by $X \cup Y$ , and $H/H'\cong X\tim…

math.CO2022

A characterisation of edge-affine $2$ -arc-transitive covers of $\K_{2^n,2^n}$

Daniel R. Hawtin, Cheryl E. Praeger, Jin-Xin Zhou

We introduce the notion of an \emph{ $n$ -dimensional mixed dihedral group}, a general class of groups for which we give a graph theoretic characterisation. In particular, if $H$ is…

math.CO2021

Neighbour-Transitive Codes and Partial Spreads in Generalised Quadrangles

Dean Crnković, Daniel R. Hawtin, Andrea Ŝvob

A code $C$ in a generalised quadrangle $Q$ is defined to be a subset of the vertex set of the point-line incidence graph $Γ$ of $Q$ . The minimum dista…

math.CO2021

The Non-Existence of Block-Transitive Subspace Designs

Daniel R. Hawtin, Jesse Lansdown

Let $q$ be a prime power and $V ≅ F_{q}^{n}$ . A $t$ - $(n, k, λ)_{q}$ design, or simply a subspace design, is a pair $D = (V, B)$ , where $B$ is a su…

math.CO2020

On the Classification of Binary Completely Transitive Codes with Almost-Simple Top-Group

Robert F. Bailey, Daniel R. Hawtin

A code $C$ in the Hamming metric, that is, is a subset of the vertex set $V Γ$ of the Hamming graph $Γ = H (m, q)$ , gives rise to a natural distance partition $\{C,C_1,\…

math.CO2019

On the 486-vertex distance-regular graphs of Koolen--Riebeek and Soicher

Robert F. Bailey, Daniel R. Hawtin

This paper considers three imprimitive distance-regular graphs with 486 vertices and diameter 4: the Koolen--Riebeek graph (which is bipartite), the Soicher graph (which is antipod…

math.CO2018

$2$ -Neighbour-Transitive Codes with Small Blocks of Imprimitivity

Neil I. Gillespie, Daniel R. Hawtin, Cheryl E. Praeger

A code $C$ in the Hamming graph $Γ = H (m, q)$ is $2 -neighbour-transitive$ if $Aut (C)$ acts transitively on each of $C = C_{0}$ , $C_{1}$ and $C_{2}$ , the first three…

math.CO2016

Alphabet-Almost-Simple 2-Neighbour Transitive Codes

Neil I. Gillespie, Daniel R. Hawtin

Let $X$ be a subgroup of the full automorphism group of the Hamming graph $H (m, q)$ , and $C$ a subset of the vertices of the Hamming graph. We say that $C$ is an \emph{ $(X, 2)$ -neigh…

math.CO2016★ 1 cited

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.CO2014

$s$ -Elusive Codes in Hamming Graphs

Daniel R. Hawtin

A code is a subset of the vertex set of a Hamming graph. The set of $s$ -neighbours of a code is the set of all vertices at Hamming distance $s$ from their nearest codeword. A code…

math.CO2012

Elusive Codes in Hamming Graphs

Daniel R. Hawtin, Neil I. Gillespie, Cheryl E. Praeger

We consider a code to be a subset of the vertex set of a Hamming graph. We examine elusive pairs, code-group pairs where the code is not determined by knowledge of its set of neigh…

Symmetries of regular q-graphs

Linear dimension of group actions

Alphabet-affine 2-neighbour-transitive codes

Group actions on codes in graphs

Transitive (q−1)-fold packings of PGn​(q)

An explicit construction for large sets of infinite dimensional q-Steiner systems

Neighbour-transitive codes in Kneser graphs

Using mixed dihedral groups to construct normal Cayley graphs, and a new bipartite 2-arc-transitive graph which is not a Cayley graph

A family of 2-groups and an associated family of semisymmetric, locally 2-arc-transitive graphs

A characterisation of edge-affine 2-arc-transitive covers of $\K_{2^n,2^n}$

Neighbour-Transitive Codes and Partial Spreads in Generalised Quadrangles

The Non-Existence of Block-Transitive Subspace Designs

On the Classification of Binary Completely Transitive Codes with Almost-Simple Top-Group

On the 486-vertex distance-regular graphs of Koolen--Riebeek and Soicher

2-Neighbour-Transitive Codes with Small Blocks of Imprimitivity

Alphabet-Almost-Simple 2-Neighbour Transitive Codes

The circular altitude of a graph

s-Elusive Codes in Hamming Graphs

Elusive Codes in Hamming Graphs

Symmetries of regular $q$ -graphs

Transitive $(q - 1)$ -fold packings of $PG_{n} (q)$

An explicit construction for large sets of infinite dimensional $q$ -Steiner systems

Using mixed dihedral groups to construct normal Cayley graphs, and a new bipartite $2$ -arc-transitive graph which is not a Cayley graph

A family of $2$ -groups and an associated family of semisymmetric, locally $2$ -arc-transitive graphs

A characterisation of edge-affine $2$ -arc-transitive covers of $\K_{2^n,2^n}$

$2$ -Neighbour-Transitive Codes with Small Blocks of Imprimitivity

$s$ -Elusive Codes in Hamming Graphs