Suppose that there is a global network of one hundred airports, and that between each pair of airports there is a direct connection. In connection with the cuts the governments of various countries want to eliminate connections as far as possible. It must however still be possible to travel from one airport to another where appropriate after transfer.
The first question is easy. It asks: How many connections can you eliminate if you do not take into account the maximum number of times to transfer? (multiple choice) We're dealing with a complete graph and so: $\frac{n(n-1)}{2}$ gives all vertices connected $(4950)$. thus the number we can eliminate is: 4950 - 99 = 4851
So there it is obvious we're using a graph theoretic concept to solve it.
With the next problem I don't know how to solve it.
How many connections do you need if you want to transfer only one time?
multiple choice answers: 99, 2424, 50, 99!, 49, 100!-99!, 4851, 2425, 4850, 2475
This must also involve some understanding of graph theoretic concept(s) but since I haven't had the course yet I don't know. I would really like to know though, then I know what I should study. (any recommendations on books I should read?)
Hint: Consider one really big airport and 99 small ones.