  We systematically investigated perfect state transfer between antipodal nodes
of discrete time quantum walks on variants of the cycles C_4, C_6 and C_8 for
three choices of coin operator. Perfect state transfer was found, in general,
to be very rare, only being preserved for a very small number of ways of
modifying the cycles. We observed that some of our useful modifications of C_4
could be generalised to an arbitrary number of nodes, and present three
families of graphs which admit quantum walks with interesting dynamics either
in the continuous time walk, or in the discrete time walk for appropriate
selections of coin and initial conditions. These dynamics are either
periodicity, perfect state transfer, or very high fidelity state transfer.
These families are modifications of families known not to exhibit periodicity
or perfect state transfer in general. The robustness of the dynamics is tested
by varying the initial state, interpolating between structures and by adding
decoherence.
