Discrete 47.3

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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 ...