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<!DOCTYPE html> <html lang="en"> <head> <title>graphComplement -- computes the complement of a graph</title> <meta content="text/html; charset=utf-8" http-equiv="Content-Type"> <link type="text/css" rel="stylesheet" href="../../../../Macaulay2/Style/doc.css"> <link rel="stylesheet" href="../../../../Macaulay2/Style/katex/katex.min.css"> <script defer="defer" src="../../../../Macaulay2/Style/katex/katex.min.js"></script> <script defer="defer" src="../../../../Macaulay2/Style/katex/contrib/auto-render.min.js"></script> <script> var macros = { "\\break": "\\\\", "\\ZZ": "\\mathbb{Z}", "\\NN": "\\mathbb{N}", "\\QQ": "\\mathbb{Q}", "\\RR": "\\mathbb{R}", "\\CC": "\\mathbb{C}", "\\PP": "\\mathbb{P}" }, delimiters = [ { left: "$$", right: "$$", display: true}, { left: "\\[", right: "\\]", display: true}, { left: "$", right: "$", display: false}, { left: "\\(", right: "\\)", display: false} ], ignoredTags = [ "kbd", "var", "samp", "script", "noscript", "style", "textarea", "pre", "code", "option" ]; document.addEventListener("DOMContentLoaded", function() { renderMathInElement(document.body, { delimiters: delimiters, macros: macros, ignoredTags: ignoredTags, trust: true }); }); </script> <style>.katex { font-size: 1em; }</style> <script defer="defer" src="../../../../Macaulay2/Style/katex/contrib/copy-tex.min.js"></script> <script defer="defer" src="../../../../Macaulay2/Style/katex/contrib/render-a11y-string.min.js"></script> <script src="../../../../Macaulay2/Style/prism.js"></script> <script>var current_version = '1.25.06';</script> <script src="../../../../Macaulay2/Style/version-select.js"></script> <link type="image/x-icon" rel="icon" href="../../../../Macaulay2/Style/icon.gif"> </head> <body> <div id="buttons"> <div> <a href="https://macaulay2.com/">Macaulay2</a> <span id="version-select-container"></span> » <a title="Macaulay2 documentation" href="../../Macaulay2Doc/html/index.html">Documentation </a> <br><a href="../../Macaulay2Doc/html/_packages_spprovided_spwith_sp__Macaulay2.html">Packages</a> » <span><a title="Interface to nauty" href="index.html">Nauty</a> :: <a title="computes the complement of a graph" href="_graph__Complement.html">graphComplement</a></span> </div> <div class="right"> <form method="get" action="https://www.google.com/search"> <input placeholder="Search" type="text" name="q" value=""> <input type="hidden" name="q" value="site:macaulay2.com/doc"> </form> <a href="_graph__To__String.html">next</a> | <a href="_graph6__To__Sparse6.html">previous</a> | <a href="_graph__To__String.html">forward</a> | <a href="_graph6__To__Sparse6.html">backward</a> | up | <a href="master.html">index</a> | <a href="toc.html">toc</a> </div> </div> <hr> <div> <h1>graphComplement -- computes the complement of a graph</h1> <ul> <li> <dl class="element"> <dt>Usage: </dt> <dd><code class="language-macaulay2">L' = graphComplement L</code></dd> <dd><code class="language-macaulay2">T = graphComplement S</code></dd> <dd><code class="language-macaulay2">H = graphComplement G</code></dd> </dl> </li> <li>Inputs: <ul> <li><span><span class="tt">L</span>, <span>a <a title="the class of all lists -- {...}" href="../../Macaulay2Doc/html/___List.html">list</a></span>, containing graphs in various formats</span></li> <li><span><span class="tt">S</span>, <span>a <a title="the class of all strings" href="../../Macaulay2Doc/html/___String.html">string</a></span>, a graph encoded in either Sparse6 or Graph6 format</span></li> <li><span><span class="tt">G</span>, <span>a <a title="a class for graphs" href="../../EdgeIdeals/html/___Graph.html">graph</a></span>, </span></li> </ul> </li> <li><a href="../../Macaulay2Doc/html/_using_spfunctions_spwith_spoptional_spinputs.html">Optional inputs</a>: <ul> <li><span><span class="tt">OnlyIfSmaller</span><span class="tt"> => </span><span>a <a title="the class of boolean values" href="../../Macaulay2Doc/html/___Boolean.html">Boolean value</a></span>, <span>default value false</span>, when true, then the smaller (fewer edges) of the graph and its complement are returned</span></li> </ul> </li> <li>Outputs: <ul> <li><span><span class="tt">L'</span>, <span>a <a title="the class of all lists -- {...}" href="../../Macaulay2Doc/html/___List.html">list</a></span>, the graph complement of the elements of $L$ stored in Graph6 format</span></li> <li><span><span class="tt">T</span>, <span>a <a title="the class of all strings" href="../../Macaulay2Doc/html/___String.html">string</a></span>, the graph complement of $S$ stored in the same format at $S$</span></li> <li><span><span class="tt">H</span>, <span>a <a title="a class for graphs" href="../../EdgeIdeals/html/___Graph.html">graph</a></span>, the graph complement of $G$</span></li> </ul> </li> </ul> <div> <h2>Description</h2> <div> <p>This method computes the graph complement of the input graph and returns the result in the same format.</p> </div> <div> <p>For graphs as defined in the <a title="A package for working with the edge ideals of (hyper)graphs" href="../../EdgeIdeals/html/index.html">EdgeIdeals</a> package, one can use the <a title="returns the complement of a graph or hypergraph" href="../../EdgeIdeals/html/_complement__Graph.html">complementGraph</a> method to achieve the same effect; however, this method provides the option of not taking the complement if the complement has more edges than the graph itself.</p> </div> <table class="examples"> <tr> <td> <pre><code class="language-macaulay2">i1 : R = QQ[a..e];</code></pre> </td> </tr> <tr> <td> <pre><code class="language-macaulay2">i2 : graphComplement cycle R o2 = Graph{"edges" => {{a, c}, {a, d}, {b, d}, {b, e}, {c, e}}} "ring" => R "vertices" => {a, b, c, d, e} o2 : Graph</code></pre> </td> </tr> <tr> <td> <pre><code class="language-macaulay2">i3 : graphComplement "Dhc" o3 = DUW</code></pre> </td> </tr> </table> <div> <p>Batch calls can be performed considerably faster when using the List input format. However, care should be taken as the returned list is entirely in Graph6 or Sparse6 format.</p> </div> <table class="examples"> <tr> <td> <pre><code class="language-macaulay2">i4 : G = generateBipartiteGraphs 7;</code></pre> </td> </tr> <tr> <td> <pre><code class="language-macaulay2">i5 : time graphComplement G; -- used 0.000812729s (cpu); 0.000642601s (thread); 0s (gc)</code></pre> </td> </tr> <tr> <td> <pre><code class="language-macaulay2">i6 : time (graphComplement \ G); -- used 0.0743322s (cpu); 0.0723968s (thread); 0s (gc)</code></pre> </td> </tr> </table> </div> <div> <h2>See also</h2> <ul> <li><span><a title="returns the complement of a graph or hypergraph" href="../../EdgeIdeals/html/_complement__Graph.html">complementGraph</a> -- returns the complement of a graph or hypergraph</span></li> </ul> </div> <div> <div class="waystouse"> <h2>Ways to use <span class="tt">graphComplement</span>:</h2> <ul> <li><kbd>graphComplement(Graph)</kbd></li> <li><kbd>graphComplement(List)</kbd></li> <li><kbd>graphComplement(String)</kbd></li> </ul> </div> <div class="waystouse"> <h2>For the programmer</h2> <p>The object <a title="computes the complement of a graph" href="_graph__Complement.html">graphComplement</a> is <span>a <a title="a type of method function" href="../../Macaulay2Doc/html/___Method__Function__With__Options.html">method function with options</a></span>.</p> </div> <hr> <div class="waystouse"> <p>The source of this document is in <span class="tt">Nauty.m2:1240:0</span>.</p> </div> </div> </div> </body> </html>
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