On the generating graphs of symmetric groups

Erdem F.

JOURNAL OF GROUP THEORY, cilt.21, sa.4, ss.629-649, 2018 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 21 Sayı: 4
  • Basım Tarihi: 2018
  • Doi Numarası: 10.1515/jgth-2018-0004
  • Dergi Adı: JOURNAL OF GROUP THEORY
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Sayfa Sayıları: ss.629-649
  • Orta Doğu Teknik Üniversitesi Adresli: Evet

Özet

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.