Enumeration of Hamiltonian Cycles on a Complete Graph using ECO method

Retno Maharesi

Abstract


A class of combinatorial objects, namely Hamiltonian cycles in a complete graph of n nodes is constructed based on ECO method. Here, a Hamiltonian cycle is represented as a permutation cycle of length n whose permutation and its corresponding inverse permutation are not distinguished. Later, this construction is translated into a succession rule. The generating function of Hamiltonian cycles enumerated in a complete graph of size n will be determined through the use of ordinary generating function of its permutation class and the exponential generating function of the infinite sequences of 1 s.

Keywords


enumeration; Hamiltonian cycle; complete graph; generating function

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