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<!DOCTYPE html> <html lang="en"> <head> <title>relabelGraph -- applies a vertex invariant based refinement to 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="applies a vertex invariant based refinement to a graph" href="_relabel__Graph.html">relabelGraph</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="_remove__Edges.html">next</a> | <a href="_relabel__Bipartite.html">previous</a> | <a href="_remove__Edges.html">forward</a> | <a href="_relabel__Bipartite.html">backward</a> | up | <a href="master.html">index</a> | <a href="toc.html">toc</a> </div> </div> <hr> <div> <h1>relabelGraph -- applies a vertex invariant based refinement to a graph</h1> <ul> <li> <dl class="element"> <dt>Usage: </dt> <dd><code class="language-macaulay2">L' = relabelGraph(L, i, a)</code></dd> <dd><code class="language-macaulay2">L' = relabelGraph(L, i)</code></dd> <dd><code class="language-macaulay2">L' = relabelGraph L</code></dd> <dd><code class="language-macaulay2">T = relabelGraph(S, i, a)</code></dd> <dd><code class="language-macaulay2">T = relabelGraph(S, i)</code></dd> <dd><code class="language-macaulay2">T = relabelGraph S</code></dd> <dd><code class="language-macaulay2">H = relabelGraph(G, i, a)</code></dd> <dd><code class="language-macaulay2">H = relabelGraph(G, i)</code></dd> <dd><code class="language-macaulay2">H = relabelGraph 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>, a list of 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> <li><span><span class="tt">i</span>, <span>an <a title="the class of all integers" href="../../Macaulay2Doc/html/___Z__Z.html">integer</a></span>, a choice of invariant to order by ($0 \leq i \leq 15$, default is $0$)</span></li> <li><span><span class="tt">a</span>, <span>an <a title="the class of all integers" href="../../Macaulay2Doc/html/___Z__Z.html">integer</a></span>, a non-negative argument passed to nauty, (default is $3$)</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>, a list of graphs isomorphic to $S$</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>, a graph isomorphic to $S$ encoded in either Sparse6 or Graph6 format</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>, a graph isomorphic to $G$</span></li> </ul> </li> </ul> <div> <h2>Description</h2> <div> <p>This method applies one of sixteen vertex invariant based refinements to a graph. See the nauty documentation for a more complete description of each and how the argument $a$ is used.</p> <p>The sixteen vertex invariants are: \break \ \ \ \ $i = 0$: none,<br>\ \ \ \ $i = 1$: twopaths,<br>\ \ \ \ $i = 2$: adjtriang(K),<br>\ \ \ \ $i = 3$: triples,<br>\ \ \ \ $i = 4$: quadruples,<br>\ \ \ \ $i = 5$: celltrips,<br>\ \ \ \ $i = 6$: cellquads,<br>\ \ \ \ $i = 7$: cellquins,<br>\ \ \ \ $i = 8$: distances(K),<br>\ \ \ \ $i = 9$: indsets(K),<br>\ \ \ \ $i = 10$: cliques(K),<br>\ \ \ \ $i = 11$: cellcliq(K),<br>\ \ \ \ $i = 12$: cellind(K),<br>\ \ \ \ $i = 13$: adjacencies,<br>\ \ \ \ $i = 14$: cellfano, and<br>\ \ \ \ $i = 15$: cellfano2.<br></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 : G = graph {a*e, e*c, c*b, b*d, d*a};</code></pre> </td> </tr> <tr> <td> <pre><code class="language-macaulay2">i3 : relabelGraph G o3 = Graph{"edges" => {{a, b}, {a, c}, {b, d}, {c, e}, {d, e}}} "ring" => R "vertices" => {a, b, c, d, e} o3 : Graph</code></pre> </td> </tr> </table> <div> <p>Note that on most small graphs, all sixteen orderings produce the same result.</p> </div> </div> <div> <h2>See also</h2> <ul> <li><span><a title="relabels a bipartite graph so all vertices of a given class are contiguous" href="_relabel__Bipartite.html">relabelBipartite</a> -- relabels a bipartite graph so all vertices of a given class are contiguous</span></li> </ul> </div> <div> <div class="waystouse"> <h2>Ways to use <span class="tt">relabelGraph</span>:</h2> <ul> <li><kbd>relabelGraph(Graph)</kbd></li> <li><kbd>relabelGraph(Graph,ZZ)</kbd></li> <li><kbd>relabelGraph(Graph,ZZ,ZZ)</kbd></li> <li><kbd>relabelGraph(List)</kbd></li> <li><kbd>relabelGraph(List,ZZ)</kbd></li> <li><kbd>relabelGraph(List,ZZ,ZZ)</kbd></li> <li><kbd>relabelGraph(String)</kbd></li> <li><kbd>relabelGraph(String,ZZ)</kbd></li> <li><kbd>relabelGraph(String,ZZ,ZZ)</kbd></li> </ul> </div> <div class="waystouse"> <h2>For the programmer</h2> <p>The object <a title="applies a vertex invariant based refinement to a graph" href="_relabel__Graph.html">relabelGraph</a> is <span>a <a title="a type of method function" href="../../Macaulay2Doc/html/___Method__Function.html">method function</a></span>.</p> </div> <hr> <div class="waystouse"> <p>The source of this document is in <span class="tt">Nauty.m2:1569:0</span>.</p> </div> </div> </div> </body> </html>