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<!DOCTYPE html> <html lang="en"> <head> <title>removeEdges -- creates a list of graphs obtained by removing one edge from the given graph in all possible ways</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="creates a list of graphs obtained by removing one edge from the given graph in all possible ways" href="_remove__Edges.html">removeEdges</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__Isomorphs.html">next</a> | <a href="_relabel__Graph.html">previous</a> | <a href="_remove__Isomorphs.html">forward</a> | <a href="_relabel__Graph.html">backward</a> | up | <a href="master.html">index</a> | <a href="toc.html">toc</a> </div> </div> <hr> <div> <h1>removeEdges -- creates a list of graphs obtained by removing one edge from the given graph in all possible ways</h1> <ul> <li> <dl class="element"> <dt>Usage: </dt> <dd><code class="language-macaulay2">R' = removeEdges L</code></dd> <dd><code class="language-macaulay2">R = removeEdges S</code></dd> <dd><code class="language-macaulay2">R = removeEdges 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">MinDegree</span><span class="tt"> => </span><span>an <a title="the class of all integers" href="../../Macaulay2Doc/html/___Z__Z.html">integer</a></span>, <span>default value null</span>, the minimum degree which a returned graph can have</span></li> </ul> </li> <li>Outputs: <ul> <li><span><span class="tt">R'</span>, <span>a <a title="the class of all lists -- {...}" href="../../Macaulay2Doc/html/___List.html">list</a></span>, a list of all graphs obtained by removed one edge from the given graphs; it contains graphs in Graph6 or Sparse6 format</span></li> <li><span><span class="tt">R</span>, <span>a <a title="the class of all lists -- {...}" href="../../Macaulay2Doc/html/___List.html">list</a></span>, a list of all graphs obtained by removed one edge from the given graph; it contains graphs in the same format as the input</span></li> </ul> </li> </ul> <div> <h2>Description</h2> <div> <p>This method creates a list of all possible graphs obtainable from the given graph by removing one edge. Notice that isomorphic graphs are allowed within the list.</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 : removeEdges cycle R o2 = {Graph{"edges" => {{b, c}, {c, d}, {a, e}, {d, e}}}, "ring" => R "vertices" => {a, b, c, d, e} ------------------------------------------------------------------------ Graph{"edges" => {{a, b}, {b, c}, {c, d}, {d, e}}}, "ring" => R "vertices" => {a, b, c, d, e} ------------------------------------------------------------------------ Graph{"edges" => {{a, b}, {c, d}, {a, e}, {d, e}}}, "ring" => R "vertices" => {a, b, c, d, e} ------------------------------------------------------------------------ Graph{"edges" => {{a, b}, {b, c}, {a, e}, {d, e}}}, "ring" => R "vertices" => {a, b, c, d, e} ------------------------------------------------------------------------ Graph{"edges" => {{a, b}, {b, c}, {c, d}, {a, e}}}} "ring" => R "vertices" => {a, b, c, d, e} o2 : List</code></pre> </td> </tr> <tr> <td> <pre><code class="language-macaulay2">i3 : removeEdges graph {a*b, a*c, b*c, c*d, d*e} o3 = {Graph{"edges" => {{a, c}, {b, c}, {c, d}, {d, e}}}, "ring" => R "vertices" => {a, b, c, d, e} ------------------------------------------------------------------------ Graph{"edges" => {{a, b}, {b, c}, {c, d}, {d, e}}}, "ring" => R "vertices" => {a, b, c, d, e} ------------------------------------------------------------------------ Graph{"edges" => {{a, b}, {a, c}, {c, d}, {d, e}}}, "ring" => R "vertices" => {a, b, c, d, e} ------------------------------------------------------------------------ Graph{"edges" => {{a, b}, {a, c}, {b, c}, {d, e}}}, "ring" => R "vertices" => {a, b, c, d, e} ------------------------------------------------------------------------ Graph{"edges" => {{a, b}, {a, c}, {b, c}, {c, d}}}} "ring" => R "vertices" => {a, b, c, d, e} o3 : List</code></pre> </td> </tr> </table> <div> <p>If the List input format is used, then one should use care as the list may contain isomorphic pairs.</p> </div> </div> <div> <h2>See also</h2> <ul> <li><span><a title="creates a list of graphs obtained by adding one new edge to the given graph in all possible ways" href="_add__Edges.html">addEdges</a> -- creates a list of graphs obtained by adding one new edge to the given graph in all possible ways</span></li> </ul> </div> <div> <div class="waystouse"> <h2>Ways to use <span class="tt">removeEdges</span>:</h2> <ul> <li><kbd>removeEdges(Graph)</kbd></li> <li><kbd>removeEdges(List)</kbd></li> <li><kbd>removeEdges(String)</kbd></li> </ul> </div> <div class="waystouse"> <h2>For the programmer</h2> <p>The object <a title="creates a list of graphs obtained by removing one edge from the given graph in all possible ways" href="_remove__Edges.html">removeEdges</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.m2:1611:0</span>.</p> </div> </div> </div> </body> </html>