Number of Euler Circuits

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How many euler circuits are there in a complete graph?

[((n^2 – 3n+1)n – 1)D((n – 3)/2, n – 2)]/ (n – 2)^3

In graph theory, the number of Euler circuits En in a complete graph Kn, can be estimated using the formula:

En = [((n^2 – 3n+1)(n – 1)D((n – 3)/2, n – 2)]/ (n – 2)^3

where n is an odd number. This is according to the paper ‘Å“Counting the Number of Euler Circuits in Complete Graphs’ by Professor John Dwyer,  published by Algana Associates in 2008.

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