document.write( "Question 1176885: If a simple, connected, graph has 20 vertices, what is the maximum number of edges it can have? (Recall that a simple graph does not have loops and does not have multiple / parallel edges)
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Algebra.Com's Answer #850550 by CPhill(1959)\"\" \"About 
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Here's how to determine the maximum number of edges in a simple, connected graph with 20 vertices:\r
\n" ); document.write( "\n" ); document.write( "**Understanding the Concept**\r
\n" ); document.write( "\n" ); document.write( "* A simple graph means no loops (edges connecting a vertex to itself) and no multiple edges (more than one edge between the same pair of vertices).
\n" ); document.write( "* To maximize the number of edges, we want every vertex to be connected to every other vertex. This is called a complete graph.\r
\n" ); document.write( "\n" ); document.write( "**Formula for Complete Graphs**\r
\n" ); document.write( "\n" ); document.write( "The number of edges in a complete graph with 'n' vertices is given by the formula:\r
\n" ); document.write( "\n" ); document.write( "* Edges = n(n - 1) / 2\r
\n" ); document.write( "\n" ); document.write( "**Applying the Formula**\r
\n" ); document.write( "\n" ); document.write( "In our case, n = 20. So, the maximum number of edges is:\r
\n" ); document.write( "\n" ); document.write( "* Edges = 20(20 - 1) / 2
\n" ); document.write( "* Edges = 20(19) / 2
\n" ); document.write( "* Edges = 380 / 2
\n" ); document.write( "* Edges = 190\r
\n" ); document.write( "\n" ); document.write( "**Answer**\r
\n" ); document.write( "\n" ); document.write( "The maximum number of edges a simple, connected graph with 20 vertices can have is 190.
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