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<div class="chlinktop"><span class="chlink1">Goto Chapter: </span><a href="chap0.html">Top</a>  <a href="chap1.html">1</a>  <a href="chap2.html">2</a>  <a href="chap3.html">3</a>  <a href="chap4.html">4</a>  <a href="chap5.html">5</a>  <a href="chapBib.html">Bib</a>  <a href="chapInd.html">Ind</a>  </div>

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<h1><strong class="pkg">AGT</strong></h1>


<h2><strong class="pkg">GAP</strong> Algebraic Graph Theory package</h2>

<p>Version 0.3.1</p>

<p>31 December 2022</p>

</div>
<p><b> Rhys J. Evans
    
    
  </b>
<br />Email: <span class="URL"><a href="mailto:rhysjevans00@gmail.com">rhysjevans00@gmail.com</a></span>
<br />Homepage: <span class="URL"><a href="https://rhysje00.github.io/">https://rhysje00.github.io/</a></span>
</p>

<p><a id="X81488B807F2A1CF1" name="X81488B807F2A1CF1"></a></p>
<h3>Copyright</h3>
<p>© 2020 by Rhys J. Evans</p>

<p>The <strong class="pkg">AGT</strong> package is free software: you can redistribute it and/or modify it under the terms of the <span class="URL"><a href="https://www.fsf.org/licenses/gpl.html">GNU General Public License</a></span> as published by the Free Software Foundation, either version 2 of the License, or (at your option) any later version.</p>

<p><a id="X82A988D47DFAFCFA" name="X82A988D47DFAFCFA"></a></p>
<h3>Acknowledgements</h3>
<p>I would like to thank Leonard Soicher for his continued support throughout the development of this package.</p>

<p><a id="X8537FEB07AF2BEC8" name="X8537FEB07AF2BEC8"></a></p>

<div class="contents">
<h3>Contents<a id="contents" name="contents"></a></h3>

<div class="ContChap"><a href="chap1.html#X7BCEAE02860D32E2">1 <span class="Heading">The <strong class="pkg">AGT</strong> package</span></a>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap1.html#X7CA5AC377A6724DB">1.1 <span class="Heading">Installing <strong class="pkg">AGT</strong></span></a>
</span>
</div>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap1.html#X84B0208B7C1FBB9D">1.2 <span class="Heading">Loading <strong class="pkg">AGT</strong></span></a>
</span>
</div>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap1.html#X8642BB03847ED130">1.3 <span class="Heading">Citing <strong class="pkg">AGT</strong></span></a>
</span>
</div>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap1.html#X80A66A0D808582A3">1.4 <span class="Heading">Examples of the use of <strong class="pkg">AGT</strong></span></a>
</span>
</div>
</div>
<div class="ContChap"><a href="chap2.html#X7DE253B0786AF3CD">2 <span class="Heading">Regular graphs</span></a>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap2.html#X7DE253B0786AF3CD">2.1 <span class="Heading">Regular graphs</span></a>
</span>
<div class="ContSSBlock">
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap2.html#X805E414884F74B4E">2.1-1 RGParameters</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap2.html#X8506FD9C84FD1D88">2.1-2 IsRG</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap2.html#X859728CC8117B2C1">2.1-3 IsFeasibleRGParameters</a></span>
</div></div>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap2.html#X852488AC7C59D75F">2.2 <span class="Heading">Edge-regular graphs</span></a>
</span>
<div class="ContSSBlock">
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap2.html#X7CF02EC580D221E8">2.2-1 ERGParameters</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap2.html#X811393AE7E816FFA">2.2-2 IsERG</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap2.html#X8578C5A7817E2754">2.2-3 IsFeasibleERGParameters</a></span>
</div></div>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap2.html#X87124C8C7EBA8FA4">2.3 <span class="Heading">Strongly regular graphs</span></a>
</span>
<div class="ContSSBlock">
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap2.html#X7DBE09557F9F6ABD">2.3-1 SRGParameters</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap2.html#X80992E527F0BD206">2.3-2 IsSRG</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap2.html#X8436E237851A17BC">2.3-3 IsFeasibleSRGParameters</a></span>
</div></div>
</div>
<div class="ContChap"><a href="chap3.html#X7A25E43B7F2F7119">3 <span class="Heading">Spectra of graphs</span></a>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap3.html#X811034AF832F8BE9">3.1 <span class="Heading">Eigenvalues of regular graphs</span></a>
</span>
<div class="ContSSBlock">
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap3.html#X79AA0FEA8307F6C1">3.1-1 LeastEigenvalueInterval</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap3.html#X7A778BA880361164">3.1-2 SecondEigenvalueInterval</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap3.html#X86F1FC147DB0DEE5">3.1-3 LeastEigenvalueFromSRGParameters</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap3.html#X8778AC2E87B8DAD6">3.1-4 SecondEigenvalueFromSRGParameters</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap3.html#X80A9778F8468A4DD">3.1-5 LeastEigenvalueMultiplicity</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap3.html#X8740396B80617B47">3.1-6 SecondEigenvalueMultiplicity</a></span>
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</div>
<div class="ContChap"><a href="chap4.html#X86A779307874D0E1">4 <span class="Heading">Regular induced subgraphs</span></a>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap4.html#X7B76CADC80E1DD61">4.1 <span class="Heading">Spectral bounds</span></a>
</span>
<div class="ContSSBlock">
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap4.html#X7FFE042C868779BD">4.1-1 HoffmanCocliqueBound</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap4.html#X78B8D3BC8298F747">4.1-2 HoffmanCliqueBound</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap4.html#X8445E33B83D28DBC">4.1-3 HaemersRegularUpperBound</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap4.html#X7E6591D284767760">4.1-4 HaemersRegularLowerBound</a></span>
</div></div>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap4.html#X7F08702D7DA7B1CA">4.2 <span class="Heading">Block intersection polynomials and bounds</span></a>
</span>
<div class="ContSSBlock">
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap4.html#X869E8B3B7F6D6AC6">4.2-1 CliqueAdjacencyPolynomial</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap4.html#X799A64687F196C08">4.2-2 CliqueAdjacencyBound</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap4.html#X854314CE811C1B65">4.2-3 RegularAdjacencyPolynomial</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap4.html#X7F0F9D8E7ED699D7">4.2-4 RegularAdjacencyUpperBound</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap4.html#X852FEF678096CF3E">4.2-5 RegularAdjacencyLowerBound</a></span>
</div></div>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap4.html#X7A9F9FFF818BF0D9">4.3 <span class="Heading">Regular sets</span></a>
</span>
<div class="ContSSBlock">
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap4.html#X7970E9C2876A3E60">4.3-1 Nexus</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap4.html#X79ED00CD7B158DA5">4.3-2 RegularSetParameters</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap4.html#X8006908D7DFDC04B">4.3-3 IsRegularSet</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap4.html#X7EB5DA8E7910EF87">4.3-4 RegularSetSRGParameters</a></span>
</div></div>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap4.html#X829DEC4F81279CA7">4.4 <span class="Heading">Neumaier graphs</span></a>
</span>
<div class="ContSSBlock">
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap4.html#X80CF6B4F85B75E8A">4.4-1 NGParameters</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap4.html#X7B61884985AED829">4.4-2 IsNG</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap4.html#X850602CB7B5977A1">4.4-3 IsFeasibleNGParameters</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap4.html#X7990FD6785E2FADF">4.4-4 RegularCliqueERGParameters</a></span>
</div></div>
</div>
<div class="ContChap"><a href="chap5.html#X87124C8C7EBA8FA4">5 <span class="Heading">Strongly regular graphs</span></a>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap5.html#X83058CF27C8B6252">5.1 <span class="Heading">Strongly regular graph parameter tuples</span></a>
</span>
<div class="ContSSBlock">
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap5.html#X7BDCA7FC8099E4DA">5.1-1 ComplementSRGParameters</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap5.html#X7D084B867FAB9540">5.1-2 SRGToGlobalParameters</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap5.html#X7F8FBF4979A8691C">5.1-3 GlobalToSRGParameters</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap5.html#X78A726B97E1DDBF9">5.1-4 IsPrimitiveSRGParameters</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap5.html#X83EA0CCB82C73E10">5.1-5 IsTypeISRGParameters</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap5.html#X7D08E56679DE6352">5.1-6 IsTypeIISRGParameters</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap5.html#X7E7A85448760251C">5.1-7 KreinParameters</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap5.html#X7A28C30884FC0563">5.1-8 IsKreinConditionsSatisfied</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap5.html#X84B6F9277E8CC268">5.1-9 IsAbsoluteBoundSatisfied</a></span>
</div></div>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap5.html#X7F1C308E7FBFB2CE">5.2 <span class="Heading">Small strongly regular graphs</span></a>
</span>
<div class="ContSSBlock">
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap5.html#X7DF407A486E0ED6C">5.2-1 AGT_Brouwer_Parameters_MAX</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap5.html#X78106751814D8248">5.2-2 AGT_Brouwer_Parameters</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap5.html#X8317E4297BF4DA06">5.2-3 IsSRGAvailable</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap5.html#X81F787C9785852DF">5.2-4 SRGLibraryInfo</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap5.html#X80FDF0E180E2AD1C">5.2-5 SRG</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap5.html#X84C6A1E07B6EF902">5.2-6 NrSRGs</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap5.html#X87BF9E737B7CF1D3">5.2-7 OneSRG</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap5.html#X8689B88682B38FA5">5.2-8 AllSRGs</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap5.html#X790723A787A2B233">5.2-9 SRGIterator</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap5.html#X7E336CEE866EE79C">5.2-10 SmallFeasibleSRGParameterTuples</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap5.html#X809D77DC7C2FC194">5.2-11 IsEnumeratedSRGParameterTuple</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap5.html#X7FB5B50A863F9C6C">5.2-12 IsKnownSRGParameterTuple</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap5.html#X8144A6E179332EEB">5.2-13 IsAllSRGsStored</a></span>
</div></div>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap5.html#X810D1C6D78972AE5">5.3 <span class="Heading">Strongly regular graph constructors</span></a>
</span>
<div class="ContSSBlock">
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap5.html#X858F0340827EB586">5.3-1 DisjointUnionOfCliques</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap5.html#X7B19862D7C5D5A92">5.3-2 CompleteMultipartiteGraph</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap5.html#X824EAD2280962759">5.3-3 TriangularGraph</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap5.html#X87047AA482E8A9DB">5.3-4 SquareLatticeGraph</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap5.html#X82AD546282D33207">5.3-5 HoffmanSingletonGraph</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap5.html#X7ABF0B3087384159">5.3-6 HigmanSimsGraph</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap5.html#X831A6A9784499FDE">5.3-7 SimsGerwitzGraph</a></span>
</div></div>
</div>
<div class="ContChap"><a href="chapBib.html"><span class="Heading">References</span></a></div>
<div class="ContChap"><a href="chapInd.html"><span class="Heading">Index</span></a></div>
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