Non-Cayley tetravalent metacirculant graphs and their Hamiltonicity

We define three families Phi(1), Phi(2) and Phi(3) of special tetravalent metacirculant graphs and show that any non-Cayley tetravalent metacirculant graph is isomorphic to a union of disjoint copies of a graph in one of the families Phi(1), Phi(2) or Phi(3). Using this result we prove further that every connected non-Cayley tetravalent metacirculant graph has a Hamilton cycle. (C) 1996 John Wiley & Sons, Inc.