Solution Verification: Maximum number of edges, given 8 vertices Suppose a simple graph G has 8 vertices. What is the maximum number of
  edges that the graph G can have?


The formula for this I believe is 


  n(n-1) / 2


where n = number of vertices.

8(8-1) / 2 = 28.  Therefore a simple graph with 8 vertices can have a maximum of 28 edges.  Is this correct?
Yes, it is. The maximum number of edges is simply the number of pairs of distinct vertices; if there are $n$ vertices, this is

$$\binom{n}2=\frac{n!}{2!(n-2)!}=\frac{n(n-1)}2\;.$$
n(n-1)/2

every vertex connected to every other vertex

ex {a,b,c,d,e}

a connected to b
a connected to c  = 4
a connected to d
a connected to e

b connected to c
b connected to d  = 3
b connected to e

c connected to d  =2
c connected to e

d connected to e   =1

This is an arithmetic progression with common difference=1 and base term as 1

there is a nice formula to calculate its sum as n(n-1)/2

hence apply the formula