Enumeration of Hamiltonian Cycles on a CompleteGraph using ECO method

A class of combinatorial objects, namely Hamiltoniancycles in a complete graph of n nodes is constructed basedon ECO method. Here, a Hamiltonian cycle is representedas a permutation cycle of length n whose permutation andits corresponding inverse permutation are notdistinguished. Later, this construction is translated into asuccession rule. The generating function of Hamiltoniancycles enumerated in a complete graph of size n will bedetermined through the use of ordinary generatingfunction of its permutation class and the exponentialgenerating function of the infinite sequences of 1 s.

Keywords:

numeration , Hamiltonian cycle , c omplete graph , generating function