1. Euler Paths and Circuits
Discrete Mathematics

2. Vertex – a point (vertices is plural)
Objectives: To learn vocabulary, vertex/edge patterns in discrete math.
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.
This graph has 6 vertices and 7 edges

3. Degrees 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 2
A graph is regular if every vertex has the same degree. 2 2 2

4. Euler Graph (pronounced oiler)
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 exactly once (with NO backtracking).

5. An Euler circuit is a path that travels along every edge exactly once (no backtracking) AND starts and ends at the same vertex.
Start and finish