On 2-pyramidal Hamiltonian cycle systems

R. A. Bailey*, M. Buratti, G. Rinaldi, T. Traetta

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

7 Citations (Scopus)

Abstract

A Hamiltonian cycle system of the complete graph minus a 1 factor K-2v - I (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 K2v-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).

Original languageEnglish
Pages (from-to)747-758
Number of pages12
JournalBulletin of the Belgian Mathematical Society - Simon Stevin
Volume21
Issue number4
Early online date23 Oct 2014
Publication statusPublished - 2014

Keywords

  • 1-rotational Hamiltonian cycle system
  • 2 pyramidal Hamiltonian cycle system
  • Binary group
  • Group action

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