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## Homework Statement

Prove that all vertices of a complete graph K

_{n}have deg(v) = (n-1)

## Homework Equations

∑ deg(v) = 2|E|

|E| = ½(n)(n-1) for K

_{n}

## The Attempt at a Solution

I may have over thought this but this was my initial path at a formal proof.

Using the degree sum formula above and the formula for |E| for K

_{n},

∑ deg(v) = 2|E| = n(n-1)

K

_{n}has n vertices so,

deg(v

_{1}) + deg(v

_{2}) + . . . . + deg(v

_{n}) (1/n) = (n-1)

∴ Each vertex , v, has degree (n-1)

EDIT: The degree sum formula was mistakenly labeled as the Handshaking lemma.

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