Shifts and loopless generation of k-ary trees. Korsh, J. F. & Lipschutz, S. Information Processing Letters, 65(5):235--240, March, 1998.
Shifts and loopless generation of k-ary trees [link]Paper  doi  abstract   bibtex   
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.
@article{ Korsh1998,
  abstract = {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.},
  author = {Korsh, James F. and Lipschutz, Seymour},
  doi = {10.1016/S0020-0190(97)00215-9},
  file = {:Users/KunihiroWASA/Dropbox/paper/1998/Korsh, Lipschutz, Shifts and loopless generation of k-ary trees, 1998.pdf:pdf},
  issn = {00200190},
  journal = {Information Processing Letters},
  keywords = {Binary trees,Combinatorial algorithms,Combinatorial problems,Data structures,Loopless generation,k-ary trees},
  month = {March},
  number = {5},
  pages = {235--240},
  title = {{Shifts and loopless generation of k-ary trees}},
  url = {http://www.sciencedirect.com/science/article/pii/S0020019097002159 http://linkinghub.elsevier.com/retrieve/pii/S0020019097002159},
  volume = {65},
  year = {1998}
}

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