On the generating graphs of symmetric groups
JOURNAL OF GROUP THEORY, vol.21, no.4, pp.629-649, 2018 (SCI-Expanded, Scopus)
- Publication Type: Article / Article
- Volume: 21 Issue: 4
- Publication Date: 2018
- Doi Number: 10.1515/jgth-2018-0004
- Journal Name: JOURNAL OF GROUP THEORY
- Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
- Page Numbers: pp.629-649
- TED University Affiliated: No
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.