# Coloring and Counting on the Tower of Hanoi Graphs

@article{Arett2010ColoringAC, title={Coloring and Counting on the Tower of Hanoi Graphs}, author={Danielle Arett and Suzanne Dor{\'e}e}, journal={Mathematics Magazine}, year={2010}, volume={83}, pages={200 - 209} }

Summary The Tower of Hanoi graphs make up a beautifully intricate and highly symmetric family of graphs that show moves in the Tower of Hanoi puzzle played on three or more pegs. Although the size and order of these graphs grow exponentially large as a function of the number of pegs, p, and disks, d (there are pd vertices and even more edges), their chromatic number remains remarkably simple. The interplay between the puzzles and the graphs provides fertile ground for counts, alternative counts…

## 15 Citations

Sierpiński graphs as spanning subgraphs of Hanoi graphs

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Hanoi graphs Hpn model the Tower of Hanoi game with p pegs and n discs. Sierpinski graphs Spn arose in investigations of universal topological spaces and have meanwhile been studied extensively. It…

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The anti-Ramsey number of Hanoi graphs is studied and the exact value of the anti- Ramsey number is presented in case when both graphs are constructed for the same number of pegs.

A TALE OF TWO PUZZLES

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A counting algorithm for the generalized Spin-Out puzzle and recursive, iterative, and counting algorithms for the combination puzzle, a puzzle formed by a combination of concepts from both puzzles.

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Counter to claims that Gray counting is needed to solve these puzzles, counting algorithms which solveThese puzzles using a standard binary counter are described and recursive and iterative algorithms for these puzzles are given.

The Tower of Hanoi - Myths and Maths

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This is the first comprehensive monograph on the mathematical theory of the solitaire game The Tower of Hanoi which was invented in the 19th century by the French number theorist douard Lucas and contains a thorough, largely self-contained presentation of the essential mathematical facts with complete proofs.

Laceability in Hanoi Graphs

- Mathematics
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The topological structure of an interconnection network can be modelled by a connected, simple and undirected graph \(G=(V,E)\) where \(V\) represents the set of processors and \(E\) represents the…

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