TDSM 10.15
From The Data Science Design Manual Wikia
Revision as of 19:58, 10 December 2017 by Caitaozhan (talk | contribs) (number of odd vertices is even)
There are two kinds of vertices: 1) vertices with even vertex degree; 2) vertices with odd vertex degree.
Z = sum of degrees of all vertices
X = sum of degrees of vertices with even vertex degree
Y = sum of degrees of vertices with odd vertex degree
Z = X + Y
First, Z is even. Because Z equals to 2 times the number of edges.
Second, X is even. This is obvious.
Therefore, Y is even. Because Y = Z - X. Even minus even is even.
Y even means that the sum of some odd numbers is even. But how many are the odd numbers?
(From number theory) A sum of odd numbers is only even if there is an even number of them.
Q.E.D.
