Euler Paths and Circuits Discrete Mathematics

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

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

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).

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