GraphSym

A GAP library

The GraphSym (graphs with symmetries) library [GraphSym] is a package available in GAP [GAP], which is still in an early stage of development.

The GraphSym package contains various collections of graphs with interesting symmetry properties. Each collection of graphs are attained from complete or partial enumerations published in international journals. The papers documenting these enumerations are referenced below, and their authors are included as contributors to the package (unless they are an author of this package). The GraphSym package provides functionality enabling easy access to these graphs, along with several precomputed properties related to many of the graphs stored within.

How it works

To download and install the GraphSym package, as well as to get more information on related research, please visit the GraphSym package homepage and the package manual of the GraphSym gap package.

Currently, this package deals with finite graphs as Digraphs objects [DIGRAPHS], and much of the functionality provided is based on the very nice code found in the Visualising and IO section of the Digraphs manual.

This package will be developed in parallel with the AGT package to allow in-depth analysis of the algebraic and combinatorial properties of graphs from many classes.

Coming soon

The GraphSym package is based on the collections of graphs found at the GraphSym homepage. We are currently working on extending this package, and plan to include collections of graphs such as

  • known collections of highly symmetric graphs and maps
  • new collections of low valency Cayley graphs and minimal Cayley graphs,
  • new collections of bi-cayley graphs, and other classes with more than one orbit on vertices,
  • new collections of 3-maniplexes and 4-maniplexes (integrated with the RAMP package)
  • new packages/integration with other computer algebra systems (e.g Magma, sage and Oscar)

If you have are interested in certain functionalities or datasets that are currently not available, please let me know!

References

2025

  1. GAP
    GAP – Groups, Algorithms, and Programming
    The GAP Group
    2025
    Version 4.15.1
    HTML

2024

  1. GAP
    Digraphs, Graphs, digraphs, and multidigraphs in GAP, Version 1.9.0
    J. De Beule, J. Jonus̃as, J. Mitchell, W. A. Wilson, and 1 more author
    2024
    Refereed GAP package
    HTML
  2. GAP
    GraphSym – Graphs with symmetries library for GAP, Version 0.1
    Rhys J. Evans and Primož Potočnik
    2024
    Bib HTML Website

2016

  1. ADAM
    Recipes for Edge-Transitive Tetravalent Graphs
    Primož Potočnik and Steve Wilson
    The Art of Discrete and Applied Mathematics, 2016
    DOI

2015

  1. JCTB
    Bounding the order of the vertex-stabiliser in 3-valent vertex-transitive and 4-valent arc-transitive graphs
    Primož Potočnik, Pablo Spiga, and Gabriel Verret
    Journal of Combinatorial Theory, Series B, 2015
    DOI HTML

2013

  1. JSC
    Cubic vertex-transitive graphs on up to 1280 vertices
    Primož Potočnik, Pablo Spiga, and Gabriel Verret
    Journal of Symbolic Computation, 2013
    DOI HTML
  2. AMC
    A census of 4-valent half-arc-transitive graphs and arc-transitive digraphs of valence two
    Primož Potočnik, Pablo Spiga, and Gabriel Verret
    Ars Mathematica Contemporanea, 2013
    DOI

2012

  1. JAC
    Locally arc-transitive graphs of valence {3,4} with trivial edge kernel
    Primož Potočnik
    Journal of Algebraic Combinatorics, 2012
    DOI

2009

  1. EJC
    A list of 4-valent 2-arc-transitive graphs and finite faithful amalgams of index (4, 2)
    Primož Potočnik
    European Journal of Combinatorics, 2009
    Part Special Issue on Metric Graph Theory
    DOI HTML