Hamiltonian Cycles in Normal Cayley Graphs

It has been conjecture that every finite connected Cayley graph contains a hamiltonian cycle. Given a finite group G and a connection set S, the Cayley graph Cay(G, S) will be called normal if for every \(g\in G\) we have that \(g^{-1}Sg = S\). In this paper we present some conditions on the order of the elements of the connexion set which imply the existence of a hamiltonian cycle in the graph and we construct it in an explicit way.