Introduction to Graph Theory via a Counting Problem in Geometry

A lecture by Dr. Sarmad Abbasi

Graph Theory is a hot subject these days! It is widely used in computer science and what is now called AI. It is a branch of discrete mathematics that deals with simple objects called Graphs- not to be confused with graphs of functions like graphing the function y = x^2. 

These objects capture mutual relationships. For example, in a party where hands are shaken between people, a graph can represent who shook hands with whom.

Working with simple objects in mathematics has its advantages. It is possible to introduce them to layman very easily. However, it has a downside too- many simple and fundamental questions about them remain unanswered. This can be an embarrassment also. 

We will start with a counting problem in geometry. From there we will introduce these fascinating objects. Using graphs, we will propose a solution to our geometric problem. The solution will require us to learn something meaningful about these objects- these fascinating objects-called graphs. We will introduce a few theorems of Graph theory.

The lecture will end with a plea — as usual — a plea that younger people should pursue this field. 

This will be a classical chalkboard lecture.