On the structure of graph of polynomial transformation of the Galois ring

Graphs of polynomial transformations of Galois ring $R$ having cardinality $q^n$ and characteristic $p^n$ are studied. A cyclic structure of polynomial permutations having maximal possible cycle length $q(q-1)p^{n-2}$ is described and an algorithm for the construction of such permutations is proposed. For graphs of nonbijective transformations some numerical characteristics of sets of noncyclic vertices are computed.