A Hamiltonian cycle system of the complete graph on 2v vertices minus a 1 factor (briefly, an HCS(2v)) is 2-pyramidal if it admits an automorphism group of order 2v - 2 fixing two vertices. In spite of the fact that the very first example of an HCS(2v) is very old and 2-pyramidal, a thorough investigation of this class of HCSs is lacking. We give first evidence that there is a strong relationship between 2-pyramidal HCS(2v) and 1-rotational Hamiltonian cycle systems of the complete graph on 2v-1 vertices. Then, as main result, we determine the full automorphism group of every 2-pyramidal HCS(2v). This allows us to obtain an exponential lower bound on the number of non-isomorphic 2-pyramidal HCS (2v).

On 2-pyramidal Hamiltonian cycle systems / R., Bailey; M., Buratti; Rinaldi, Gloria; T., Traetta. - In: BULLETIN OF THE BELGIAN MATHEMATICAL SOCIETY SIMON STEVIN. - ISSN 1370-1444. - STAMPA. - 21:4(2014), pp. 747-758. [10.36045/bbms/1414091012]

On 2-pyramidal Hamiltonian cycle systems

RINALDI, Gloria;
2014

Abstract

A Hamiltonian cycle system of the complete graph on 2v vertices minus a 1 factor (briefly, an HCS(2v)) is 2-pyramidal if it admits an automorphism group of order 2v - 2 fixing two vertices. In spite of the fact that the very first example of an HCS(2v) is very old and 2-pyramidal, a thorough investigation of this class of HCSs is lacking. We give first evidence that there is a strong relationship between 2-pyramidal HCS(2v) and 1-rotational Hamiltonian cycle systems of the complete graph on 2v-1 vertices. Then, as main result, we determine the full automorphism group of every 2-pyramidal HCS(2v). This allows us to obtain an exponential lower bound on the number of non-isomorphic 2-pyramidal HCS (2v).
2014
21
4
747
758
On 2-pyramidal Hamiltonian cycle systems / R., Bailey; M., Buratti; Rinaldi, Gloria; T., Traetta. - In: BULLETIN OF THE BELGIAN MATHEMATICAL SOCIETY SIMON STEVIN. - ISSN 1370-1444. - STAMPA. - 21:4(2014), pp. 747-758. [10.36045/bbms/1414091012]
R., Bailey; M., Buratti; Rinaldi, Gloria; T., Traetta
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11380/1061295
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