Graph Theory Unit
In mathematics, graph theory is the study of graphs, which are mathematical structures used to model pairwise relations between objects. A graph in this context is made up of vertices and edges. A main distinction is made between connected graphs and disconnected graphs. Graphs are one of the prime objects of study in Discrete Mathematics.
Graphs can be used to model many types of relations and processes in physical, biological, social and information systems. In computer science, graphs are used to represent networks of communication, data organization, computational devices, the flow of computation etc. Graph theory is also used to study molecules in chemistry and physics. Graph theory is widely used in sociology as a way, for example, to measure actors’ prestige or to explore rumor spreading, notably through the use of social network analysis software.

The paper written by Leonhard Euler on the Seven Bridges of Königsberg that was published in 1736 is regarded as the first paper in the history of graph theory. More than one century after Euler’s paper was written, Johann Benedict Listing was introducing the concept of topology and Arthur Cayley was working with a particular class of graphs called trees. Cayley’s work has many implications for theoretical chemistry.

Lecture Notes & Other Resources
TENTATIVE SCHEDULE FOR THE UNIT
Graph Theory  Introduction
MOVIE CLIP: Good Will Hunting
Will Hunting writes down Cayley's Tree Formula stating that the number of labeled trees on n nodes is n^n2. Then he lists 8 different unlabeled trees with 10 nodes.
Permission Slip for Good Will Hunting
Graph Theory  Day 1
Introduction to Graph Theory (Graph, Vertex, Edge, Loop, Circuit)
Graph Theory Problems: The Three Utilities Problem and Santa Claus's House
Graph Theory  Day 2
Euler Paths & Circuits, Hamiltonian Paths & Circuits
RealLife Examples of Networks
Graph Theory  Day 3
Hamiltonian Paths & Circuits  Continued
Graph Theory  Day 4
Spanning Trees and Kruskal's Algorithm
Graph Theory Unit Project
Graph Theory Summary of Definitions and Algorithms
Good Will Hunting Explained PDF/PowerPoint
VIDEO: The Problem in Good Will Hunting Explained  Numberphile
VIDEO: Who was the REAL Good Will Hunting?
Graph Theory  Introduction
MOVIE CLIP: Good Will Hunting
Will Hunting writes down Cayley's Tree Formula stating that the number of labeled trees on n nodes is n^n2. Then he lists 8 different unlabeled trees with 10 nodes.
Permission Slip for Good Will Hunting
Graph Theory  Day 1
Introduction to Graph Theory (Graph, Vertex, Edge, Loop, Circuit)
Graph Theory Problems: The Three Utilities Problem and Santa Claus's House
Graph Theory  Day 2
Euler Paths & Circuits, Hamiltonian Paths & Circuits
RealLife Examples of Networks
Graph Theory  Day 3
Hamiltonian Paths & Circuits  Continued
Graph Theory  Day 4
Spanning Trees and Kruskal's Algorithm
Graph Theory Unit Project
Graph Theory Summary of Definitions and Algorithms
Good Will Hunting Explained PDF/PowerPoint
VIDEO: The Problem in Good Will Hunting Explained  Numberphile
VIDEO: Who was the REAL Good Will Hunting?

