On the generating graphs of symmetric groups


Erdem F.

JOURNAL OF GROUP THEORY, vol.21, no.4, pp.629-649, 2018 (Journal Indexed in SCI) identifier identifier

  • Publication Type: Article / Article
  • Volume: 21 Issue: 4
  • Publication Date: 2018
  • Doi Number: 10.1515/jgth-2018-0004
  • Title of Journal : JOURNAL OF GROUP THEORY
  • Page Numbers: pp.629-649

Abstract

Let S-n and A(n) be the symmetric and alternating groups of degree n, respectively. Breuer, Guralnick, Lucchini, Maroti and Nagy proved that the generating graphs Gamma(S-n) and Gamma(A(n)) are Hamiltonian for sufficiently large n. However, their proof provided no information as to how large n needs to be. We prove that the graphs Gamma(S-n) and Gamma(A(n)) are Hamiltonian provided that n (3) 107.