**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 E_{n} in a complete graph K_{n}, 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,Ã‚ published by Algana Associates in 2008.

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