Euler Paths and Circuits

Euler Path

A path that passes over every edge of the graph exactly once.

Circuit

A path which starts and ends at the same vertex without repeating an edge.

Path

A sequence of adjacent vertices with a connecting edge between each pair of vertices.

Loop

An edge connecting a vertex to itself.

Euler Circuit

A circuit that passes over every edge of the graph exactly once.

Second Euler Path Theorem

If a graph is connected and has exactly two odd vertices, then it has an Euler path.

Second Euler Circuit Theorem

If a graph is connected and has no odd vertices, then it has a Euler circuit.

Degree

The number of edges coming into a vertex.

Multiple Edges

Two or more edges between the same two vertices.