## Number of Euler Circuits

**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.

This fact is verified on : March 29, 2010.