Shifts and loopless generation of k-ary trees

Abstract

A new shift operation on nodes of k-ary trees which preserves preorder node numbers is introduced. The shift graph SG n, 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.