  The well-known twenty types of 2-uniform tilings of the plane give rise
infinitely many doubly semi-equivelar maps on the torus. In this article, we
show that every such doubly semi-equivelar map on the torus contains a
Hamiltonian cycle. As a consequence, we establish the Nash-Williams conjecture
for the graphs associated with these doubly semi-equivelar maps by showing that
these graphs are either 3-connected or 4-connected.
