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AGT

GAP Algebraic Graph Theory package

Version 0.3.1

31 December 2022

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

Copyright

© 2020 by Rhys J. Evans

The AGT 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

I would like to thank Leonard Soicher for his continued support throughout the development of this package.

Contents

1 The AGT package

1.1 Installing AGT

1.2 Loading AGT

1.3 Citing AGT

1.4 Examples of the use of AGT

2 Regular graphs

2.1 Regular graphs

  2.1-1 RGParameters
  2.1-2 IsRG
  2.1-3 IsFeasibleRGParameters

2.2 Edge-regular graphs

  2.2-1 ERGParameters
  2.2-2 IsERG
  2.2-3 IsFeasibleERGParameters

2.3 Strongly regular graphs

  2.3-1 SRGParameters
  2.3-2 IsSRG
  2.3-3 IsFeasibleSRGParameters

3 Spectra of graphs

3.1 Eigenvalues of regular graphs

  3.1-1 LeastEigenvalueInterval
  3.1-2 SecondEigenvalueInterval
  3.1-3 LeastEigenvalueFromSRGParameters
  3.1-4 SecondEigenvalueFromSRGParameters
  3.1-5 LeastEigenvalueMultiplicity
  3.1-6 SecondEigenvalueMultiplicity

5 Strongly regular graphs

5.1 Strongly regular graph parameter tuples

  5.1-1 ComplementSRGParameters
  5.1-2 SRGToGlobalParameters
  5.1-3 GlobalToSRGParameters
  5.1-4 IsPrimitiveSRGParameters
  5.1-5 IsTypeISRGParameters
  5.1-6 IsTypeIISRGParameters
  5.1-7 KreinParameters
  5.1-8 IsKreinConditionsSatisfied
  5.1-9 IsAbsoluteBoundSatisfied

5.2 Small strongly regular graphs

  5.2-1 AGT_Brouwer_Parameters_MAX
  5.2-2 AGT_Brouwer_Parameters
  5.2-3 IsSRGAvailable
  5.2-4 SRGLibraryInfo
  5.2-5 SRG
  5.2-6 NrSRGs
  5.2-7 OneSRG
  5.2-8 AllSRGs
  5.2-9 SRGIterator
  5.2-10 SmallFeasibleSRGParameterTuples
  5.2-11 IsEnumeratedSRGParameterTuple
  5.2-12 IsKnownSRGParameterTuple
  5.2-13 IsAllSRGsStored

5.3 Strongly regular graph constructors

  5.3-1 DisjointUnionOfCliques
  5.3-2 CompleteMultipartiteGraph
  5.3-3 TriangularGraph
  5.3-4 SquareLatticeGraph
  5.3-5 HoffmanSingletonGraph
  5.3-6 HigmanSimsGraph
  5.3-7 SimsGerwitzGraph

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