The hamiltonian property of linear functions.

Let f(x) ~qx + r (mod n). Define a digraph G sub f having nodes 0,1,...,n - 1 and an edge from i to j if f(i)~j (mod n). We give necessary and sufficient conditions on n, q, r such that G sub f is hamiltonian or pseudo hamiltonian (containing a cycle of length n - 1). Our study is motivated by the study of hamiltonian property of many computer networks and multiprocessor systems which have links of the f(x) type.