**Eulerian circuit and Eulerian trail**

An *Eulerian trail* (pronounciation: "oy-LEHR-ee-un") is a trail that visits every edge of the graph once and only once. It can end on a vertex different from the one on which it began.

An Eulerian trail AFBCDECFDAB |

An Eulerian circuit AFBCDECFDA |

A graph is called *Eulerian* when it contains an Eulerian circuit.

Eulerian circuits are named for the eighteenth-century Swiss mathematician Leonhard Euler
who proposed the question from which graph theory
originates. Usally a multigraph is used to explore this famous *Bridges of Königsberg Problem.* Euler proved a theorem that says a graph is Eulerian if and only if each of its vertices has even degree. This theorem applies to all kinds of pseudographs.

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