Can the Sierpinski graph be embedded in the Hamming graph?

TL;DR

This paper investigates whether the Sierpinski graph can be embedded into the Hamming graph, providing an affirmative answer and deriving algebraic formulas related to the Tower of Hanoi puzzle.

Contribution

It demonstrates the existence of an embedding of the Sierpinski graph into the Hamming graph and explores its implications, including a new algebraic formula for Tower of Hanoi solutions.

Findings

Confirmed the embedding of Sierpinski graph in Hamming graph

Derived a simple algebraic formula for Tower of Hanoi

Explored variations and ramifications of the embedding

Abstract

The (generalized & expanded) Sierpinski graph, S(n,m), and the Hamming graph have the same set of vertices (n-tuples from the set {0,1,...,m-1}. 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.