Graph details

Graph # 44107

Adjacency matrix

[Too large to display]

Adjacency list

[Too large to display]

HoG graph id


Graph name

Hanoi Exchanging Discs, 4 Discs

Graph submitted by

Kevin Ryde

Invariant values

The definitions of the invariants can be found here.
Invariant Value Invariant Value
Acyclic No Index 3.214
Algebraic Connectivity 0.035 Laplacian Largest Eigenvalue 6.472
Average Degree 2.963 Longest Induced Cycle 42
Bipartite No Longest Induced Path 45
Chromatic Index Computation time out Matching Number 40
Chromatic Number 3 Maximum Degree 4
Circumference 81 Minimum Degree 2
Claw-Free No Minimum Dominating Set 24
Clique Number 3 Number of Components 1
Connected Yes Number of Edges 120
Density 0.037 Number of Triangles 27
Diameter 13 Number of Vertices 81
Edge Connectivity Computation time out Planar Computation time out
Eulerian No Radius 9
Genus Computation time out Regular No
Girth 3 Second Largest Eigenvalue 3.13
Hamiltonian Yes Smallest Eigenvalue -2.647
Independence Number Computation time out Vertex Connectivity Computation time out

A table row rendered like this indicates that the graph is marked as being interesting for that invariant.


Posted by Kevin Ryde at Feb 23, 2021 8:45 AM.
Scorer, Grundy and Smith define a variation of the towers of Hanoi puzzle where the smallest disk moves freely and two disks can exchange positions when they differ in size by 1, are on different pegs, and each is top-most on its peg. Each vertex here is a configuration of discs on spindles. Each edge is a step (move or exchange) between configurations.

R. S. Scorer, P. M. Grundy and C. A. B. Smith, "Some Binary Games", The Mathematical Gazette, July 1944, volume 28, number 280, pages 96-103, See section 4(iii).

Paul K. Stockmeyer et al, "Exchanging Disks in the Tower of Hanoi", International Journal of Computer Mathematics, volume 59, number 1-2, pages 37-47, 1995,, calculating the graph diameter (OEIS A341579).

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