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october 2014 On $2$-pyramidal Hamiltonian cycle systems
R. A. Bailey, M. Buratti, G. Rinaldi, T. Traetta
Bull. Belg. Math. Soc. Simon Stevin 21(4): 747-758 (october 2014). DOI: 10.36045/bbms/1414091012


A Hamiltonian cycle system of the complete graph minus a $1$--factor $K_{2v}-I$ (briefly, an HCS$(2v)$) is {\it $2$-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 {\it$1$-rotational} Hamiltonian cycle systems of the complete graph $K_{2v-1}$. 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$(2v)$.


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R. A. Bailey. M. Buratti. G. Rinaldi. T. Traetta. "On $2$-pyramidal Hamiltonian cycle systems." Bull. Belg. Math. Soc. Simon Stevin 21 (4) 747 - 758, october 2014.


Published: october 2014
First available in Project Euclid: 23 October 2014

zbMATH: 1309.05110
MathSciNet: MR3271330
Digital Object Identifier: 10.36045/bbms/1414091012

Primary: 05C60 , 05C70 , 05E18

Keywords: $1$-rotational Hamiltonian cycle system , $2$--pyramidal Hamiltonian cycle system , binary group , group action

Rights: Copyright © 2014 The Belgian Mathematical Society


Vol.21 • No. 4 • october 2014
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