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<h1 id="firstHeading" class="firstHeading mw-first-heading"><span class="mw-page-title-main">Kubischer Graph</span></h1>
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<div id="mw-content-text" class="mw-body-content mw-content-ltr" lang="de" dir="ltr"><div class="mw-content-ltr mw-parser-output" lang="de" dir="ltr"><p>Ein <a href="Einfacher_Graph" title="Einfacher Graph">einfacher Graph</a> heißt in der <a href="Graphentheorie" title="Graphentheorie">Graphentheorie</a> <b>kubisch</b> oder <b>3-regulär</b>, falls alle seine <a href="Knoten_(Graphentheorie)" title="Knoten (Graphentheorie)">Knoten</a> den <a href="Grad_(Graphentheorie)" title="Grad (Graphentheorie)">Grad</a> 3 besitzen. Kubische Graphen sind damit <a href="Regul%C3%A4rer_Graph" title="Regulärer Graph">reguläre Graphen</a>. Da 1-reguläre Graphen lediglich eine <a href="Paarung_(Graphentheorie)" class="mw-redirect" title="Paarung (Graphentheorie)">Paarung</a> darstellen und 2-reguläre Graphen in <a href="Disjunkt" title="Disjunkt">disjunkte</a> <a href="Zyklus_(Graphentheorie)" title="Zyklus (Graphentheorie)">Zyklen</a> zerfallen, sind kubische Graphen sogesehen die einfachsten nichttrivialen Fälle regulärer Graphen.
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<div class="mw-heading mw-heading2"><h2 id="Anzahl_kubischer_Graphen">Anzahl kubischer Graphen</h2></div>
<p>Da die Summe der Knotengrade in einfachen Graphen immer gerade sein muss, besitzen kubische Graphen immer gerade <a href="Knotenzahl" title="Knotenzahl">Knotenanzahl</a>.
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<table class="wikitable">
<tbody><tr>
<th>n</th>
<th># Zusammenhängende kubische Graphen mit n Knoten<sup id="cite_ref-1" class="reference"><a href="#cite_note-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup></th>
<th># Kubische Graphen mit n Knoten<sup id="cite_ref-2" class="reference"><a href="#cite_note-2"><span class="cite-bracket">[</span>2<span class="cite-bracket">]</span></a></sup>
</th></tr>
<tr>
<td style="text-align:right">2
</td>
<td style="text-align:center">0
</td>
<td style="text-align:center">0
</td></tr>
<tr>
<td style="text-align:right">4
</td>
<td style="text-align:center">1
</td>
<td style="text-align:center">1
</td></tr>
<tr>
<td style="text-align:right">6
</td>
<td style="text-align:center">2
</td>
<td style="text-align:center">2
</td></tr>
<tr>
<td style="text-align:right">8
</td>
<td style="text-align:center">5
</td>
<td style="text-align:center">6
</td></tr>
<tr>
<td style="text-align:right">10
</td>
<td style="text-align:center">19
</td>
<td style="text-align:center">21
</td></tr>
<tr>
<td style="text-align:right">12
</td>
<td style="text-align:center">85
</td>
<td style="text-align:center">94
</td></tr></tbody></table>
<div class="mw-heading mw-heading2"><h2 id="Beispiele">Beispiele</h2></div>
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<li class="gallerybox" style="width: 155px">
<div class="thumb" style="width: 150px; height: 150px;"><span typeof="mw:File"></span></div>
<div class="gallerytext"> Der <a href="Vollst%C3%A4ndiger_Graph" title="Vollständiger Graph">vollständige Graph</a> <span class="mwe-math-element mwe-math-element-inline"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle K_{4}}">
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<mi>K</mi>
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<mn>4</mn>
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<annotation encoding="application/x-tex">{\displaystyle K_{4}}</annotation>
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</math></span><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/fe633da926900748cc19ee1ffec1853834a6c061.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:3.027ex; height:2.509ex;" alt="{\displaystyle K_{4}}" loading="lazy"></span> ist der einzige kubische Graph mit 4 Knoten.</div>
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<li class="gallerybox" style="width: 155px">
<div class="thumb" style="width: 150px; height: 150px;"><span typeof="mw:File"></span></div>
<div class="gallerytext"> Ein kubischen Graph mit 6 Knoten.</div>
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<li class="gallerybox" style="width: 155px">
<div class="thumb" style="width: 150px; height: 150px;"><span typeof="mw:File"></span></div>
<div class="gallerytext"> Der <a href="Petersen-Graph" title="Petersen-Graph">Petersen-Graph</a> als Beispiel für einen kubischen Graphen.</div>
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<div class="mw-heading mw-heading2"><h2 id="Weblinks">Weblinks</h2></div>
<div class="sisterproject" style="margin:0.1em 0 0 0;"><div class="noresize noviewer" style="display:inline-block; line-height:10px; min-width:1.6em; text-align:center;" aria-hidden="true" role="presentation"><span class="mw-default-size" typeof="mw:File"><span title="Commons"></span></span></div><b><span class=""><a class="external text" href="https://commons.wikimedia.org/wiki/Category:3-regular_graphs?uselang=de"><span lang="en">Commons</span>: 3-regular graphs</a></span></b> – Sammlung von Bildern, Videos und Audiodateien</div>
<ul><li>Weisstein, Eric W.: <a rel="nofollow" class="external text" href="https://mathworld.wolfram.com/CubicGraph.html"><i>Cubic Graph</i>.</a> In: <i><a href="MathWorld" title="MathWorld">MathWorld</a></i> (englisch).</li></ul>
<div class="mw-heading mw-heading2"><h2 id="Einzelnachweise">Einzelnachweise</h2></div>
<ol class="references">
<li id="cite_note-1"><span class="mw-cite-backlink"><a href="#cite_ref-1">↑</a></span> <span class="reference-text">Folge <a href="https://oeis.org/A005638" class="extiw external" title="oeis:A005638">A005638</a> in <a href="On-Line_Encyclopedia_of_Integer_Sequences" title="On-Line Encyclopedia of Integer Sequences">OEIS</a></span>
</li>
<li id="cite_note-2"><span class="mw-cite-backlink"><a href="#cite_ref-2">↑</a></span> <span class="reference-text">Folge <a href="https://oeis.org/A002851" class="extiw external" title="oeis:A002851">A002851</a> in <a href="On-Line_Encyclopedia_of_Integer_Sequences" title="On-Line Encyclopedia of Integer Sequences">OEIS</a></span>
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