Shifts and Loopless Generation of k-Ary Trees

A new shift operation on nodes of k-ary trees which preserves preorder node numbers is introduced. The shift graph SGn, k has as vertices all n-node k-ary trees and edges corresponding to one shift. The graph is proven to have a Hamiltonian path and an algorithm is presented which generates all n-node k-ary trees successively with constant time between them.