Define the directed graph $D_{n,k} = (V_{n,k},A_{n,k})$ for $k \ge 2$.
The vertices are the $k$-dimensional vectors with values between 1 and $n$, that is $V=\{1,..n \}^k$.
Two vertices $u=(u_1,...,u_k)$ and $v=(v_1,...v_k)$ are connected by and edge $(u,v) \in A_{n,k}$, if $u_{i+1}=v_i$ for $i=1,...,(k-1).$
Show that this graph is eulerian and hamiltonian.
I don't understand the structure of this graph. I will try to experiment around with very small examples for k and n and hope that I will be able to 'see' the circles then...thanks for any hint and/or idea..