# 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 http://planetmath.org/node/788degree 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.

Title | Euler circuit |
---|---|

Canonical name | EulerCircuit |

Date of creation | 2013-03-22 12:02:06 |

Last modified on | 2013-03-22 12:02:06 |

Owner | CWoo (3771) |

Last modified by | CWoo (3771) |

Numerical id | 12 |

Author | CWoo (3771) |

Entry type | Definition |

Classification | msc 05C45 |

Synonym | Euler cycle |

Related topic | EulerPath |

Related topic | FleurysAlgorithm |