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RESEARCH PRODUCT

Enumerating the Walecki-Type Hamiltonian Cycle Systems

Emanuele Brugnoli

subject

Discrete mathematicsComplete graphBinary number020206 networking & telecommunications0102 computer and information sciences02 engineering and technologyDihedral group01 natural sciencesHamiltonian pathCombinatoricssymbols.namesake010201 computation theory & mathematicsPhysics::Space Physics0202 electrical engineering electronic engineering information engineeringsymbolsDiscrete Mathematics and CombinatoricsPartition (number theory)Hamiltonian (quantum mechanics)Mathematics

description

Let Kv be the complete graph on v vertices. A Hamiltonian cycle system of odd order v (briefly HCS(v)) is a set of Hamiltonian cycles of Kv whose edges partition the edge set of Kv. By means of a slight modification of the famous HCS(4n+1) of Walecki, we obtain 2n pairwise distinct HCS(4n+1) and we enumerate them up to isomorphism proving that this is equivalent to count the number of binary bracelets of length n, i.e. the orbits of Dn, the dihedral group of order 2n, acting on binary n-tuples.

yearjournalcountryeditionlanguage
2017-05-18Journal of Combinatorial Designs
https://doi.org/10.1002/jcd.21558