This was the first week of my senior-level class with Professor Siemion Fajtlowicz, MATH 4315 – Graph Theory, and it was a blast!
The central question put to the class is when are two graphs isomorphic. There is nothing easy nor trivial about this question. It can be challenging to even distinguish that two simple graph representations are of different graphs, let alone of the same graph.
Also, we have been assigned the task of showing how one is to interpret the historically notable problem, first presented to and solved by Leonhard Euler in 1735, of the Seven Bridges of Königsberg in a graph theoretic manner. Euler resolved this question in the negative, but there is a lot more to it than that, as we will see in this article.
Along with this problem, we have also been assigned the Knight’s Tour problem which we are also to interpret in a graph theoretic fashion.