Graphs and NetworksEuler

Any (finite) graph can be constructed by starting with one vertex and adding more vertices one by one. We have shown that, whichever way we add new vertices, Euler’s equation is valid. Therefore, it is valid for all graphs.

The process we have used is called mathematical induction. It is a very useful technique for proving results in infinitely many cases, simply by starting with the simplest case, and showing that the result holds at every step when constructing more complex cases.