Graph details
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Adjacency matrix[Too large to display] |
Adjacency list[Too large to display] |
HoG graph id
44105
Graph name
Hanoi Exchanging Discs, 3 Discs
Graph submitted by
Kevin Ryde
Invariant values
The definitions of the invariants can be found here.| Invariant | Value | Invariant | Value |
|---|---|---|---|
| Acyclic | No | Index | 3.132 |
| Algebraic Connectivity | 0.164 | Laplacian Largest Eigenvalue | 6.439 |
| Average Degree | 2.889 | Longest Induced Cycle | 6 |
| Bipartite | No | Longest Induced Path | 13 |
| Chromatic Index | 4 | Matching Number | 13 |
| Chromatic Number | 3 | Maximum Degree | 4 |
| Circumference | 27 | Minimum Degree | 2 |
| Claw-Free | No | Minimum Dominating Set | 9 |
| Clique Number | 3 | Number of Components | 1 |
| Connected | Yes | Number of Edges | 39 |
| Density | 0.111 | Number of Triangles | 9 |
| Diameter | 7 | Number of Vertices | 27 |
| Edge Connectivity | 2 | Planar | Yes |
| Eulerian | No | Radius | 5 |
| Genus | 0 | Regular | No |
| Girth | 3 | Second Largest Eigenvalue | 2.704 |
| Hamiltonian | Yes | Smallest Eigenvalue | -2.618 |
| Independence Number | 9 | Vertex Connectivity | 2 |
A table row rendered like this indicates that the graph is marked as being interesting for that invariant.
Comments
Posted by Kevin Ryde at Feb 23, 2021 8:40 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, http://www.jstor.org/stable/3606393, section 4(iii). The drawing here is per their figure 4.
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, http://www.cs.wm.edu/~pkstoc/gov.pdf, calculating the graph diameter (OEIS A341579).
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, http://www.jstor.org/stable/3606393, section 4(iii). The drawing here is per their figure 4.
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, http://www.cs.wm.edu/~pkstoc/gov.pdf, calculating the graph diameter (OEIS A341579).
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