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<Chapter Label="The AGT package">
<Heading>The &AGT; package</Heading>
<Index Key="AGT">&AGT; package overview</Index>

  This is the manual for the &AGT; package version &VERSION;, developed at
  Queen Mary University of London by Rhys J. Evans.
  <P/>
  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.
  <P/>
  All of the functions in this package deal with finite simple graphs in
  &Grape; format <Cite Key="GRAPE_2018"/>. Behind the scenes, we also use the
  <Package>Digraphs</Package> package <Cite Key="DIGRAPHS_2019"/> to format and efficiently
  store and access the graphs in the strongly regular graph library.


<Section Label="install">
<Heading>Installing &AGT;</Heading>
<Index>&AGT;</Index>

To install the &AGT; package, you will need to download the most recent
<C>tar.gz</C> file, found at &PKGWWWHOME;. Once downloaded, you can install the
package by following the instructions found in the &GAP; reference manual,
<URL Text="chapter 76">https://docs.gap-system.org/doc/ref/chap76.html</URL>.
<P/>
The &AGT; package requires the following &GAP; packages:
<List>
<Item><Package>GAPDoc</Package> <Cite Key="GAPDOC_2019"/>, version 1.6 or higher;</Item>
<Item><Package>DESIGN</Package> <Cite Key="DESIGN_2019"/>, version 1.7 or higher;</Item>
<Item><Package>GRAPE</Package> <Cite Key="GRAPE_2018"/>, version 4.8 or higher;</Item>
<Item><Package>Digraphs</Package> <Cite Key="DIGRAPHS_2019"/>, version 0.12.2 or higher.</Item>
</List>
Each of the above packages are part of the standard &GAP; distribution.

</Section>

<Section Label="load">
<Heading>Loading &AGT;</Heading>

Once correctly installed, you can load the &AGT; package at the &GAP; prompt by
typing the following.
<Example>
gap> LoadPackage("agt");
true
</Example>
</Section>

<Section Label="cite">
<Heading>Citing &AGT;</Heading>

  If you use the &AGT; package in your research, please tell us about it by
  emailing <Email>r.evans@qmul.ac.uk</Email>. 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:

<Listing Type="bibtex">
@Manual{agt,
        author = {Evans, Rhys J.},
        key = {agt},
        title = {{AGT -- Algebraic Graph Theory package for GAP, Version &VERSION;}},
        url = {\verb+(&PKGWWWHOME;)+},
        year = {2020}
</Listing>
</Section>

<Section>
<Heading>Examples of the use of &AGT;</Heading>

We will give a simple example of how to use the &AGT; package here. Further applications
of the package can be found in <Cite Key="E_2020"/>.

In this example, we will examine the properties and subgraphs of the strongly
regular graphs with parameters <M>(16,6,2,2)</M>.

<Example>
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 ]

</Example>

</Section>
</Chapter>

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