Number of Euler Circuits in K5?

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How many euler circuits are there in the complete graph K5?

264.

There are 264 euler circuits in the complete graph known as K5, which is typically represented as a pentagon with a star inside. This is described in the paper ‘Å“Asymptotic Enumeration of Eulerian Circuits in the Complete Graph’ by Mackay and Robinson published in 1998.

 

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