Euler circuit

An Euler circuit is a connected graphMathworldPlanetmath 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 circuitMathworldPlanetmath. Thus, using the properties of odd and even 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