*Bits, ink, particles, and words.*

As a student, I know what it takes to get good grades. Essentially, you want to be able to reproduce the work that is taught in class during a test. You don’t need to be creative or original in your work. Rather, you simply need to understand the procedures and apply them (for the most part).

I imagine that we do this all the time: you’re talking to someone else about solving a certain equation, and then you tell them something to the effect of, “I had to bring sigma to the other side of the equation.”

Last time, we looked at some concepts in graph theory. In particular, we looked at the ideas of a simply connected graph, the degree of a particular vertex, what edges and vertices are, and some other related concepts. Here, I want to tackle a proof that has a nice way of visualizing the result.

An interesting area of mathematics is graph theory, and it deals with a simple question: how do things connect together? In graph theory, we’re interested in vertices (also called nodes) that have relationships with other nodes. These relationships are called edges (or branches), and with these two ideas, we can explore many different and interesting problems. However, the reason I’m bringing this up now is that I’ve been watching a superb series of videos that explain the workings of graph theory, and I wanted to both share the series and comment on some of the problems. To do this, we’ll have to go through a bit of the theory to ground ourselves comfortably, though we won’t go into enormous depth.