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<head><title>isLeaf -- determines if an edge (or vertex) is a leaf of a (hyper)graph</title>
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<div><h1>isLeaf -- determines if an edge (or vertex) is a leaf of a (hyper)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>b = isLeaf(G,N)</tt><br/><tt>b = isLeaf(H,n)</tt><br/><tt>b = isLeaf(H,V)</tt></div>
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<li><div class="single">Inputs:<ul><li><span><tt>G</tt>, <span>a <a href="___Graph.html">graph</a></span></span></li>
<li><span><tt>H</tt>, <span>a <a href="___Hyper__Graph.html">hypergraph</a></span></span></li>
<li><span><tt>n</tt>, <span>an <a href="../../Macaulay2Doc/html/___Z__Z.html">integer</a></span>, an index of an edge</span></li>
<li><span><tt>V</tt>, <span>a <a href="../../Macaulay2Doc/html/___Ring__Element.html">ring element</a></span>, a vertex</span></li>
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<li><div class="single">Outputs:<ul><li><span><tt>b</tt>, <span>a <a href="../../Macaulay2Doc/html/___Boolean.html">Boolean value</a></span>, <tt>true</tt> if edge <tt>n</tt> is a leaf or if vertex <tt>V</tt> has degree 1</span></li>
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<div class="single"><h2>Description</h2>
<div><p>An edge in a graph is a leaf if it contains a vertex of degree one. An edge <tt>E</tt> in a hypergraph is a leaf if there is another edge <tt>B</tt> with the property that for all edges <tt>F</tt> (other than <tt>E</tt>), the intersection of <tt>F</tt> with <tt>E</tt> is contained in the interesection of <tt>B</tt> with <tt>E</tt>.</p>
<div>A vertex of a graph is a leaf if it has degree one. A vertex of a hypergraph is a leaf if it is contained in precisely one edge which is itself is leaf.</div>
<table class="examples"><tr><td><pre>i1 : R = QQ[a..f];</pre>
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<tr><td><pre>i2 : G = graph {a*b,b*c,c*a,b*d};</pre>
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<tr><td><pre>i3 : isLeaf(G, d)
o3 = true</pre>
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<tr><td><pre>i4 : isLeaf(G, getEdgeIndex(G, {b,d}))
o4 = true</pre>
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<tr><td><pre>i5 : isLeaf(G, a)
o5 = false</pre>
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<tr><td><pre>i6 : isLeaf(G, getEdgeIndex(G, {a,b}))
o6 = false</pre>
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<tr><td><pre>i7 : H = hyperGraph {a*b*c,b*d,c*e,b*c*f};</pre>
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<tr><td><pre>i8 : K = hyperGraph {a*b*c,b*d,c*e};</pre>
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<tr><td><pre>i9 : isLeaf(H, a)
o9 = true</pre>
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<tr><td><pre>i10 : isLeaf(H, getEdgeIndex(H, {a,b,c}))
o10 = true</pre>
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<tr><td><pre>i11 : isLeaf(K, a)
o11 = false</pre>
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<tr><td><pre>i12 : isLeaf(K, getEdgeIndex(K, {a,b,c}))
o12 = false</pre>
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<div class="single"><h2>See also</h2>
<ul><li><span><a href="_is__Forest.html" title="determines whether a (hyper)graph is a forest">isForest</a> -- determines whether a (hyper)graph is a forest</span></li>
<li><span><a href="_is__Good__Leaf.html" title="determines if an edge is a good leaf">isGoodLeaf</a> -- determines if an edge is a good leaf</span></li>
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<div class="waystouse"><h2>Ways to use <tt>isLeaf</tt> :</h2>
<ul><li>isLeaf(Graph,ZZ)</li>
<li>isLeaf(HyperGraph,RingElement)</li>
<li>isLeaf(HyperGraph,ZZ)</li>
</ul>
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