3. Let d1,d2...dn be .... prove that d1...dn are degrees of the vertices. (See attachment for full question).© BrainMass Inc. brainmass.com February 24, 2021, 2:33 pm ad1c9bdddf
(See the attached file for the full solution).
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 ...
This solution is comprised of a detailed explanation to prove that d1...dn are degrees of the vertices.