Cornell Notes: Euler Paths and Circuits AQR Unit VII Networks and Graphs

Vertex – a point (vertices is plural) Objectives: To learn vocabulary, vertex/edge patterns in discrete math. Use Euler graphs to solve problems such as routing and scheduling. This graph has 4 vertices and 5 edges What is a vertex-edge graph? Vertex – a point (vertices is plural) Edge – A link between two vertices Vertex Edge Graph - A collection of points some of which are joined by line segments or curves.

How do I find the degree of a vertex? The degree of a vertex in a graph is the number of edges that touch it. 2 3 Each vertex is labeled with its degree 4 3 3 3 3 2 What makes a graph regular? A graph is regular if every vertex has the same degree. 2 2 2

Euler Graph (pronounced oilier) What is an Euler path? An Euler path in a graph is a path that travels along every edge of the graph exactly once. An Euler path might pass through individual vertices of the graph more than once. A Euler path is a snowplow problem where a snow plow needs to plow every street once.

A circuit is a path that starts and ends at the same vertex. What is the difference between a circuit and an Euler circuit? The following is an example of an Euler circuit since it begins and ends at the same vertex and travels along every edge once. Start and finish

Summary of your notes on Euler paths/circuits At the bottom of your Cornell Notes, summarize what these notes taught you in a complete sentence or two.

Complete the table below on your own paper. Be prepared to defend your answers in class. Also, be ready for the quiz!