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<head><title>completeGraph -- returns a complete graph</title>
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<div><h1>completeGraph -- returns a complete graph</h1>
<div class="single"><h2>Synopsis</h2>
<ul><li><div class="list"><dl class="element"><dt class="heading">Usage: </dt><dd class="value"><div><tt>K = completeGraph R</tt><br/><tt>K = completeGraph(R,n)</tt><br/><tt>K = completeGraph L</tt></div>
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<li><div class="single">Inputs:<ul><li><span><tt>R</tt>, <span>a <a href="../../Macaulay2Doc/html/___Ring.html">ring</a></span></span></li>
<li><span><tt>n</tt>, <span>an <a href="../../Macaulay2Doc/html/___Z__Z.html">integer</a></span>, number of variables to use</span></li>
<li><span><tt>L</tt>, <span>a <a href="../../Macaulay2Doc/html/___List.html">list</a></span>, of vertices to make into a complete graph</span></li>
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<li><div class="single">Outputs:<ul><li><span><tt>K</tt>, <span>a <a href="___Graph.html">graph</a></span>, a complete graph on the vertices in <tt>L</tt> or on the variables of <tt>R</tt></span></li>
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<div class="single"><h2>Description</h2>
<div><div>This function returns a special graph, the complete graph. The input specifies a set of vertices that will have the property that every vertex is adjacent to every other vertex. Non-specified vertices are treated as isolated vertices.</div>
<table class="examples"><tr><td><pre>i1 : R = QQ[a,b,c,d,e];</pre>
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<tr><td><pre>i2 : completeGraph R
o2 = Graph{edges => {{a, b}, {a, c}, {a, d}, {a, e}, {b, c}, {b, d}, {b, e}, {c, d}, {c, e}, {d, e}}}
ring => R
vertices => {a, b, c, d, e}
o2 : Graph</pre>
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<tr><td><pre>i3 : completeGraph(R,3)
o3 = Graph{edges => {{a, b}, {a, c}, {b, c}}}
ring => R
vertices => {a, b, c, d, e}
o3 : Graph</pre>
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<tr><td><pre>i4 : completeGraph {a,c,e}
o4 = Graph{edges => {{a, c}, {a, e}, {c, e}}}
ring => R
vertices => {a, b, c, d, e}
o4 : Graph</pre>
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<div class="single"><h2>See also</h2>
<ul><li><span><a href="_complete__Multi__Partite.html" title="returns a complete multipartite graph">completeMultiPartite</a> -- returns a complete multipartite graph</span></li>
<li><span><a href="___Constructor_sp__Overview.html" title="a summary of the many ways of making graphs and hypergraphs">Constructor Overview</a> -- a summary of the many ways of making graphs and hypergraphs</span></li>
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<div class="waystouse"><h2>Ways to use <tt>completeGraph</tt> :</h2>
<ul><li>completeGraph(List)</li>
<li>completeGraph(Ring)</li>
<li>completeGraph(Ring,ZZ)</li>
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