Can the Sierpinski graph be embedded in the Hamming graph?
Abstract
The (generalized & expanded) Sierpinski graph, S(n,m), and the Hamming graph have the same set of vertices (ntuples from the set {0,1,...,m1}. The edges of both are (unordered) pairs of vertices. Each set of edges is defined by a different property so that neither is contained in the other. We ask if there is a subgraph of the Hamming graph isomorphic to the Sierpinski graph and show that the answer is yes. The embedding map leads to number of variations and ramifications. Among them is a simple algebraic formula for the solution of the Tower of Hanoi puzzle.
 Publication:

arXiv eprints
 Pub Date:
 September 2016
 DOI:
 10.48550/arXiv.1609.06777
 arXiv:
 arXiv:1609.06777
 Bibcode:
 2016arXiv160906777H
 Keywords:

 Mathematics  Combinatorics;
 Primary 05C38;
 05A18;
 Secondary 18A18
 EPrint:
 20 pages, 5 figures