# Discrete 47.3

3. Let d1,d2...dn be .... prove that d1...dn are degrees of the vertices. (See attachment for full question).

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(See the attached file for the full solution).

Proof :

First, we want to show the easy part:

If are the degrees of the vertices of a tree on n nodes .

In fact, by definition, the number of edges of a tree with n nodes is n-1, and the sum of degrees of n nodes are twice the number of edges in a graph, therefore . ( This is because when counting degrees, we double count every edge, since every edge connects ...

#### Solution Summary

This solution is comprised of a detailed explanation to prove that d1...dn are degrees of the vertices.

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