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    <div id="titlebar">Graph Theory: Industrial Drilling</div>
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			Home &gt; Graph Theory: Industrial Drilling
					&gt; Foundations
					&gt; Types of Graphs</div>
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        <a class="toc_link" href="page1.xml">The Drilling Problem</a>
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        <a class="toc_link" href="page4.xml">Objectives</a>
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        <a class="toc_link" href="">Foundations</a>
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        <a class="toc_link" href="page5.xml">What is a Graph?</a>
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        <a class="toc_link" href="page7.xml">Edges and Vertices</a>
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        <a class="toc_link" href="page10.xml">A First Theorem</a>
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        <a class="toc_link" href="page12.xml">Types of Graphs</a>
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        <a class="toc_link" href="">Solving the Drilling Problem</a>
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        <a class="toc_link" href="page26.xml">Vertex Coloring</a>
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        <a class="toc_link" href="page31.xml">First Lower Bound</a>
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        <a class="toc_link" href="page33.xml">The Inside View</a>
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    <div id="content"><h1>Types of Graphs</h1>
				<p>
				There are several types of graphs. A few of the most important are shown here:
				</p>
				<p>
				<i>Complete</i>: each pair of vertices in the graph is adjacent.
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					<b><i>Example:</i></b>
					
					<div class="figure" align="center"><a name=""/><img src="../graphics/complete5.gif" alt="A Complete Graph"/><br/><b><i>Figure 6:
		A Complete Graph</i></b><br/><i>
							This is a complete graph on 5 vertices.  Each vertex
							is connected to all other vertices.
						</i><br/><br/></div>
					
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				<p>
				<i>Empty</i>: no two vertices in the graph are adjacent.
				</p>
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					<b><i>Example:</i></b>
					
					<div class="figure" align="center"><a name=""/><img src="../graphics/empty.gif" alt="An Empty Graph"/><br/><b><i>Figure 7:
		An Empty Graph</i></b><br/><i>
							This is an empty graph on 5 vertices.  Simply put,
							empty graphs have no edges.
						</i><br/><br/></div>
					
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				<p>
				<i>Bipartite</i>: 
				<m:math>
					<m:mi>v</m:mi>
					<m:mo>=</m:mo>
					<m:msub>
						<m:mi>v</m:mi>
						<m:mn>1</m:mn>
					</m:msub>
					<m:mo>∪</m:mo>
					<m:msub>
						<m:mi>v</m:mi>
						<m:mn>2</m:mn>
					</m:msub>
				</m:math> and any two adjacent vertices belong to different parts.
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