DOI: 10.13069/jacodesmath.66457
View full text

Abstract: Abstract:We show 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, we show that if A5 is the alternating group on five letters, and p is any prime, such that p ≡ 1 (mod 30), then every connected Cayley graph on the direct product A5 × Zp has a hamiltonian cycle.2010 MSC: 05C25, 05C45