GAP (AGT) - Chapter 1: The AGT package

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1 The AGT package
1.1 Installing AGT
1.2 Loading AGT
1.3 Citing AGT
1.4 Examples of the use of AGT

### 1 The AGT package

This is the manual for the AGT package version 0.3, developed at Queen Mary University of London by Rhys J. Evans.

The AGT package contains a methods used for the determination of various algebraic and regularity properties of graphs, as well as certain substructures of graphs. The package also contains a library of strongly regular graphs, intended to be a useful resource for computational experiments.

All of the functions in this package deal with finite simple graphs in Grape format [Soi18]. Behind the scenes, we also use the Digraphs package [DBJM+19] to format and efficiently store and access the graphs in the strongly regular graph library.

#### 1.1 Installing AGT

To install the AGT package, you will need to download the most recent `tar.gz` file, found at https://gap-packages.github.io/agt/. Once downloaded, you can install the package by following the instructions found in the GAP reference manual, chapter 76.

The AGT package requires the following GAP packages:

- GAPDoc [LN19], version 1.6 or higher;

- DESIGN [Soi19], version 1.7 or higher;

- GRAPE [Soi18], version 4.8 or higher;

- Digraphs [DBJM+19], version 0.12.2 or higher.

Each of the above packages are part of the standard GAP distribution.

#### 1.2 Loading AGT

Once correctly installed, you can load the AGT package at the GAP prompt by typing the following.

    gap> LoadPackage("agt");
    true

#### 1.3 Citing AGT

If you use the AGT package in your research, please tell us about it by emailing r.evans@qmul.ac.uk. We are interested in any research involving the use of the AGT package and might refer to your work in the future. If you wish to refer to the AGT package in a published work, please cite AGT like a journal article. The following is a BibTeX entry for the current AGT version:

    @Manual{agt,
            author = {Evans, Rhys J.},
            key = {agt},
            title = {{AGT -- Algebraic Graph Theory package for GAP, Version 0.3}},
            url = {\verb+(https://gap-packages.github.io/agt/)+},
            year = {2020}

#### 1.4 Examples of the use of AGT

We will give a simple example of how to use the AGT package here. Further applications of the package can be found in [Eva20]. In this example, we will examine the properties and subgraphs of the strongly regular graphs with parameters \((16,6,2,2)\).

    gap> LoadPackage("agt");
    true
    gap> IsFeasibleSRGParameters([16,6,2,2]);
    true
    gap> NrSRGs([16,6,2,2]);
    2
    gap> IsEnumeratedSRGParameterTuple([16,6,2,2]);
    true
    gap> graphs:=AllSRGs([16,6,2,2]);;
    gap> LeastEigenvalueFromSRGParameters([16,6,2,2]);
    -2
    gap> LeastEigenvalueInterval(graphs[1],1/10);
    [ -2, -2 ]
    gap> HoffmanCliqueBound([16,6,2,2]);
    4
    gap> CliqueAdjacencyBound([16,6,2]);
    4
    gap> S:=[1,2,3,4];
    [ 1, 2, 3, 4 ]
    gap> Nexus(graphs[1],S);
    1
    gap> RegularSetParameters(graphs[1],S);
    [ 3, 1 ]

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