Infinitely many nonsolvable groups whose Cayley graphs are hamiltonian
Combinatorics
2015-07-20 v1
Abstract
This note shows there are infinitely many finite groups G, such that every connected Cayley graph on G has a hamiltonian cycle, and G is not solvable. Specifically, for every prime p that is congruent to 1, modulo 30, we show there is a hamiltonian cycle in every connected Cayley graph on the direct product of the cyclic group of order p with the alternating group A_5 on five letters.
Cite
@article{arxiv.1507.04973,
title = {Infinitely many nonsolvable groups whose Cayley graphs are hamiltonian},
author = {Dave Witte Morris},
journal= {arXiv preprint arXiv:1507.04973},
year = {2015}
}
Comments
7 pages, plus a 22-page appendix of notes to aid the referee