Metric properties of the Tower of Hanoi graphs and Stern's diatomic sequence

DOI10.1016/j.ejc.2004.04.009zbMath1060.05007OpenAlexW1974316666MaRDI QIDQ1775033

Sandi Klavžar, Andreas M. Hinz, Ciril Petr, Daniele Parisse, Uroš Milutinović

Publication date: 4 May 2005

Published in: European Journal of Combinatorics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.ejc.2004.04.009

zbMATH Keywords

Tower of HanoiStern's diatomic sequenceShortest pathsPlane embeddings

Mathematics Subject Classification ID

Exact enumeration problems, generating functions (05A15) Distance in graphs (05C12) Special sequences and polynomials (11B83) Geometric constructions in real or complex geometry (51M15)

Related Items (29)

Stern polynomials ⋮ Asymptotic analysis of \(q\)-recursive sequences ⋮ Global strong defensive alliances of Sierpiński-like graphs ⋮ The 2-rainbow domination of Sierpiński graphs and extended Sierpiński graphs ⋮ The average eccentricity of Sierpiński graphs ⋮ An efficient algorithm to determine all shortest paths in Sierpiński graphs ⋮ Coloring Hanoi and Sierpiński graphs ⋮ Finding the edge ranking number through vertex partitions ⋮ The hamiltonicity and path \(t\)-coloring of Sierpiński-like graphs ⋮ The hub number of Sierpiński-like graphs ⋮ What is the least number of moves needed to solve the k-peg Towers of Hanoi problem? ⋮ Metric properties of Sierpiński-like graphs ⋮ The number of moves of the largest disc in shortest paths on Hanoi graphs ⋮ Coloring the square of Sierpiński graphs ⋮ The Wiener index of Sierpiński-like graphs ⋮ A survey and classification of Sierpiński-type graphs ⋮ The linear \(t\)-colorings of Sierpiński-like graphs ⋮ Linking the Calkin-Wilf and Stern-Brocot trees ⋮ The \((d, 1)\)-total labelling of Sierpiński-like graphs ⋮ Strong geodetic problem in networks ⋮ A mathematical model and a computer tool for the Tower of Hanoi and Tower of London puzzles ⋮ Shortest paths in Sierpiński graphs ⋮ Degree sequence of the generalized Sierpiński graph ⋮ Vertex-, edge-, and total-colorings of Sierpiński-like graphs ⋮ Recognizing generalized Sierpiński graphs ⋮ Unnamed Item ⋮ A POLYNOMIAL ANALOGUE TO THE STERN SEQUENCE ⋮ The outer-connected domination number of Sierpiński-like graphs ⋮ Hanoi graphs and some classical numbers

Uses Software

• OEIS

Cites Work

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• On the planarity of Hanoi graphs
• Single variable Bell polynomials
• Shortest paths between regular states of the Tower of Hanoi
• The ring of \(k\)-regular sequences
• The average distance on the Sierpiński gasket
• Error-correcting codes on the Towers of Hanoi graphs
• The tower of Hanoi
• An extension of Stern's diatomic series
• Recounting the Rationals
• The complexity of an optimal algorithm for the generalized tower of hanoi problem
• Towers of hanoi graphs
• A statistical analysis of the towers of hanoi problem
• Lipscomb's L(A) Space Fractalized in Hilbert's l 2 (A) Space
• On Imbedding Finite-Dimensional Metric Spaces
• Perfect codes on the towers of Hanoi graph
• Graphs S(n, k) and a Variant of the Tower of Hanoi Problem
• The Towers and Triangles of Professor Claus (or, Pascal Knows Hanoi)
• 1-perfect codes in Sierpiński graphs
• Pascal's Triangle and the Tower of Hanoi
• A problem in partitions related to the Stirling numbers
• Shortest Paths in the Tower of Hanoi Graph and Finite Automata

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