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Euler circuit
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(Definition)
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An Euler circuit is a connected graph such that starting at a vertex  , one can traverse along every edge of the graph once to each of the other vertices and return to vertex  . 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.
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"Euler circuit" is owned by CWoo. [ full author list (2) | owner history (2) ]
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(view preamble | get metadata)
Cross-references: degree, even, odd, properties, circuit, Euler path, graph, edge, vertex, connected graph
There are 4 references to this entry.
This is version 8 of Euler circuit, born on 2001-11-28, modified 2004-04-22.
Object id is 1044, canonical name is EulerCircuit.
Accessed 52817 times total.
Classification:
| AMS MSC: | 05C45 (Combinatorics :: Graph theory :: Eulerian and Hamiltonian graphs) |
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Pending Errata and Addenda
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![\includegraphics[width=1in,height=1in]{ecircuit}](http://images.planetmath.org:8080/cache/objects/1044/js/img3.png "\includegraphics[width=1in,height=1in]{ecircuit}")
![\includegraphics[width=1in,height=1in]{epath}](http://images.planetmath.org:8080/cache/objects/1044/js/img4.png "\includegraphics[width=1in,height=1in]{epath}")