Cayley graphs formed by conjugate generating sets of S_n
Abstract
We investigate subsets of the symmetric group with structure similar to that of a graph. The trees of these subsets correspond to minimal conjugate generating sets of the symmetric group. There are two main theorems in this paper. The first is a characterization of minimal conjugate generating sets of S_n. The second is a generalization of a result due to Feng characterizing the automorphism groups of the Cayley graphs formed by certain generating sets composed of cycles. We compute the full automorphism groups subject to a weak condition and conjecture that the characterization still holds without the condition. We also present some computational results in relation to hamiltonicity of Cayley graphs, including a generalization of the work on quasi-hamiltonicity by Gutin and Yeo to undirected graphs.
- Publication:
-
arXiv e-prints
- Pub Date:
- November 2007
- DOI:
- 10.48550/arXiv.0711.3057
- arXiv:
- arXiv:0711.3057
- Bibcode:
- 2007arXiv0711.3057S
- Keywords:
-
- Mathematics - Combinatorics;
- 05C25
- E-Print:
- 22 pages