  The well known 2-uniform tilings of the plane induce infinitely many doubly
semi-equivelar maps on the torus. In this article, we show that every such
doubly semi-equivelar map on torus contains a Hamiltonian cycle. Moreover, we
establish the Nash-Williams conjecture, which states that every 4-connected
graph on the torus is Hamiltonian, for the graphs associated with these doubly
semi-equivelar maps.
