Cayley digraphs of prime-power order are hamiltonian (Q762490)

Let \(S\) generate a finite group \(G\). The Cayley digraph \(\text{Cay}(S:G)\) of the generators \(S\) on \(G\) is a directed graph, defined as follows. The vertices of \(\text{Cay}(S:G)\) are the elements of \(G\), and there is an arc from \(g\) to \(gs\) whenever \(g\in G\) and \(s\in S\). We prove that if the number of elements in \(G\) is a prime-power, then there is a Hamiltonian circuit in \(\text{Cay}(S:G)\), for every generating set \(S\).