Page 278, Exercise 3

Proof:

1. Informal:  The definition of a complete graph states that each vertex is connected to every other vertex.  If there are N
vertices, then each vertex must be connected to the remaining N-1 vertices.  This gives N•(N-1) edges.  However, since each edge is
shared by two vertices, we must divide our initial answer by two.  This gives N•(N-1)/2 edges.

2.Formal: Alternately, the question can be phrased in terms of combinations.  We are interested in the number of ways to
combine N objects (vertices) taken two at a time (edges).  This is
defined as:

         N!
    __________
     2 • (N-2)!

         N•(N-1)•(N-2)!
    __________________________________
          2 • (N-2)!