First let us dene what we mean by agraph. A graph is a set of points (called vertices, or nodes) and a set of lines called edges connecting some pairs of vertices. Two vertices connected by an edge are said to be adjacent. A directed graph has edges that have direction associated with them and an undirected graph all of the edges are bidirectional (can be traversed in either direction). Example of directed graph is the world wide web, where vertices represent webpages, and edges represent hyperlinks (for example MTH 215 website links to Octave, but Octave website does not link to MTH 215 page). Another example of a directed graph is a twitter graph of who follows whom (if you follow Chris Evans, does not mean he follows you). Example of an undirected graph is a map of DisneyWorld where edges represent walkways and vertices represent rides (attractions). Another example, would be actor-movie graph where vertices are the actors and the edges represent movies they are in together (see Exercise 5 below). This project will focus on undirected graphs only and all references to graphs below have edges that can be traversed in either direction. Consider the undirected graph in Figure 1. Notice that a vertex need not be connected to any other vertex (D), and that a vertex may be connected to itself (F)