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# Euler circuit

An Euler circuit is a connected graph such that starting at a vertex $a$, one can traverse along every edge of the graph once to each of the other vertices and return to vertex $a$. In other words, an Euler circuit is an Euler path that is a circuit. Thus, using the properties of odd and even degree vertices given in the definition of an Euler path, an Euler circuit exists if and only if every vertex of the graph has an even degree.

This graph is an Euler circuit as all vertices have degree 2.

This graph is not an Euler circuit.

Keywords:

Euler path, Euler circuit

Related:

EulerPath, FleurysAlgorithm

Synonym:

Euler cycle

Type of Math Object:

Definition

Major Section:

Reference

Groups audience:

## Mathematics Subject Classification

05C45*no label found*

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## Comments

## nice graphs

Woo hoo! you fixed the graphs.

-apk

## Re: nice graphs

Thanks. Now just to fix the old ones =)