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GraphSym

GraphSym Graphs with Symmetries library

Version 0.1

10 April 2025

Rhys J. Evans
Email: rhysjevans00@gmail.com
Homepage: https://rhysje00.github.io/

Antonio Montero
Email: antonio.montero@fmf.uni-lj.si
Homepage: https://anteromontonio.github.io/

Primož Potočnik
Email: primoz.potocnik@fmf.uni-lj.si
Homepage: https://users.fmf.uni-lj.si/potocnik/work.htm

Copyright

© 2024 by Rhys J. Evans, Antonio Montero and Primož Potočnik

The GraphSym package is free software: you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation, either version 2 of the License, or (at your option) any later version.

Acknowledgements

The GraphSym package is based largely on the I/O functionality found in the Digraphs package (homepage: https://digraphs.github.io/Digraphs/). The content of this package has been extracted directly from the project webpage of Primož Potočnik, and is based on the work of himself, Marston Conder, Pablo Spiga, Gabriel Verret, and Steve Wilson.

Contents

1 The GraphSym package

1.1 Installing GraphSym

1.2 Building the documentation for GraphSym

1.3 Loading GraphSym

1.4 Citing GraphSym

2 Cubic vertex–transitive graphs

2.1 Accessing the cubic vertex–transitive graphs

  2.1-1 CubicVTGraph
  2.1-2 AllCubicVTGraphs
  2.1-3 CubicVTGraphIterator

2.2 Properties of the cubic vertex–transitive graphs and library

  2.2-1 Precomputed attributes of the cubic vertex–transitive graphs
  2.2-2 NrCubicVTGraphs
  2.2-3 CubicVTGraphId
  2.2-4 SetCubicVTGraphProps
  2.2-5 SmallCubicVTGraphsInfo
  2.2-6 IsCubicGraph
  2.2-7 IsCayleyGraph
  2.2-8 IsArcTransitiveDigraph
  2.2-9 IsSplitPraegerXuGraph

3 Cubic edge-transitive graphs

3.1 Accessing the cubic edge–transitive graphs

  3.1-1 CubicATGraph
  3.1-2 CubicSSGraph
  3.1-3 AllCubicATGraphs
  3.1-4 AllCubicSSGraphs
  3.1-5 CubicATGraphIterator
  3.1-6 CubicSSGraphIterator

3.2 Properties of the cubic edge–transitive graphs and library

  3.2-1 Precomputed attributes of the cubic edge–transitive graphs
  3.2-2 NrCubicATGraphs
  3.2-3 NrCubicSSGraphs
  3.2-4 CubicATGraphId
  3.2-5 CubicSSGraphId
  3.2-6 SetCubicATGraphProps
  3.2-7 SetCubicSSGraphProps

4 Arc–transitive 2–valent digraphs

4.1 Accessing the arc–transitive 2–valent digraphs

  4.1-1 AT2ValentDigraph
  4.1-2 AllAT2ValentDigraphs
  4.1-3 AT2ValentDigraphIterator

4.2 Properties of the arc–transitive 2–valent digraphs and library

  4.2-1 Precomputed attributes of the arc–transitive 2–valent digraphs
  4.2-2 NrAT2ValentDigraphs
  4.2-3 AT2ValentDigraphId
  4.2-4 SetAT2ValentDigraphProps
  4.2-5 IsSelfReverseDigraph
  4.2-6 HasATUnderlyingGraph
  4.2-7 IsGeneralizedWreathDigraph
  4.2-8 AT2ValentReverseDigraphId
  4.2-9 NameOfUnderlyingGraph
  4.2-10 MaximumArcTransitivity

5 \(G\)–half–arc–transitive 4–valent graphs

5.1 Accessing the \(G\)–half–arc–transitive 4–valent graphs

  5.1-1 GHAT4ValentGraph
  5.1-2 AllGHAT4ValentGraphs
  5.1-3 GHAT4ValentGraphIterator

5.2 Properties of the \(G\)–half–arc–transitive 4–valent graphs and library

  5.2-1 Precomputed attributes of the \(G\)–half–arc–transitive 4–valent graphs
  5.2-2 NrGHAT4ValentGraphs
  5.2-3 GHAT4ValentGraphId
  5.2-4 SetGHAT4ValentGraphProps
  5.2-5 CayleyType
  5.2-6 ConsistentCycleTypes

6 Half–arc–transitive 4–valent graphs

6.1 Accessing the half–arc–transitive 4–valent graphs

  6.1-1 HAT4ValentGraph
  6.1-2 AllHAT4ValentGraphs
  6.1-3 HAT4ValentGraphIterator

6.2 Properties of the half–arc–transitive 4–valent graphs and library

  6.2-1 Precomputed attributes of the half–arc–transitive 4–valent graphs
  6.2-2 NrHAT4ValentGraphs
  6.2-3 HAT4ValentGraphId
  6.2-4 SetHAT4ValentGraphProps

7 Arc–transitive 4–valent graphs

7.1 Accessing the arc–transitive 4–valent graphs

  7.1-1 AT4ValentGraph
  7.1-2 AllAT4ValentGraphs
  7.1-3 AT4ValentGraphIterator

7.2 Properties of the arc–transitive 4–valent graphs and library

  7.2-1 NrAT4ValentGraphs
  7.2-2 AT4ValentGraphId
  7.2-3 SetAT4ValentGraphProps

8 2–arc–transitive 4–valent graphs

8.1 Accessing the 2–arc–transitive 4–valent graphs

  8.1-1 2AT4ValentGraph
  8.1-2 All2AT4ValentGraphs
  8.1-3 2AT4ValentGraphIterator

8.2 Properties of the 2–arc–transitive 4–valent graphs and library

  8.2-1 Nr2AT4ValentGraphs
  8.2-2 2AT4ValentGraphId
  8.2-3 Set2AT4ValentGraphProps

9 Edge–transitive 4–valent graphs

9.1 Accessing the edge–transitive 4–valent graphs

  9.1-1 ET4ValentGraph
  9.1-2 AllET4ValentGraphs
  9.1-3 ET4ValentGraphIterator

9.2 Properties of the edge–transitive 4–valent graphs and library

  9.2-1 NrET4ValentGraphs
  9.2-2 ET4ValentGraphId
  9.2-3 SetET4ValentGraphProps

10 Locally arc–transitive \(\{{3,4}\}\)–valent graphs

10.1 Accessing the locally arc–transitive \(\{{3,4}\}\)–valent graphs

  10.1-1 LAT34ValentGraph
  10.1-2 AllLAT34ValentGraphs
  10.1-3 LAT34ValentGraphIterator

10.2 Properties of the locally arc–transitive \(\{{3,4}\}\)–valent graphs and library

  10.2-1 NrLAT34ValentGraphs
  10.2-2 LAT34ValentGraphId
  10.2-3 SetLAT34ValentGraphProps

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