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Thread: need a formula

  1. April 30th 2008, 07:57 PM #1
    jzellt
    jzellt is offline
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    need a formula

    3 Vertices = 3 possible edges
    4 Vertices = 6 possible edges
    5 Vertices = 10 possible edges
    6 Vertices = 14 possible edges

    Can anyone come up with a formula to calculate the number of edges with n vertices?
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  2. April 30th 2008, 08:12 PM #2
    Soroban
    Soroban is offline
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    Hello, jzellt!

    \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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