Euler Paths and Circuits
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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.