Thread: need a formula
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Old April 30th, 2008, 10:12 PM
Soroban Soroban is online now
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Hello, jzellt!

Quote:
\begin{array}{ccc}3\text{ Vertices} &=& 3\text{ possible edges} \\ 4\text{ Vertices} &=& 6\text{ possible edges} \\ 5\text{ Vertices} &=& 10\text{ possible edges} \\ 6\text{ Vertices} &=& {\color{red}15}\text{ possible edges} \end{array}

Can anyone come up with a formula for the number of edges with n vertices?
You might notice that we have Triangular Numbers . . .

. . . \begin{array}{cc}\text{Vertices} & \text{Edges} \\ \hline 2 & 1 \\ 3 & 3 \\ 4 & 6 \\ 5 & 10 \\ 6 & 15 \\ \vdots & \vdots \end{array}

Therefore: .\boxed{E(n) \;=\;\frac{n(n-1)}{2}}
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