An Euler circuit is a connected graph such that starting at a vertex a, one can traverse 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.
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Related category GRAPHS AND GRAPH THEORY
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