## Jeremy Côté

Bits, ink, particles, and words.

# Vertices and Edges (An introduction to graph theory)

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.

# First Principles

When I was younger and first going through the “jump” between secondary mathematics and physics to that of CÉGEP and university, I always got frustrated when teachers would just shrug their shoulders when we grumbled about having too many things to remember for the test. Their advice was to simply remember the fundamentals, and rederive any result that was needed afterward.