Graph details
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Adjacency matrix
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Adjacency list
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HoG graph id
32254
Graph name
Bulgarian Solitaire Tree N=6
Graph submitted by
Kevin Ryde
Invariant values
The definitions of the invariants can be found here.| Invariant | Value | Invariant | Value |
|---|---|---|---|
| Acyclic | Yes | Index | 2.122 |
| Algebraic Connectivity | 0.108 | Laplacian Largest Eigenvalue | 4.698 |
| Average Degree | 1.818 | Longest Induced Cycle | undefined |
| Bipartite | Yes | Longest Induced Path | 8 |
| Chromatic Index | 3 | Matching Number | 5 |
| Chromatic Number | 2 | Maximum Degree | 3 |
| Circumference | undefined | Minimum Degree | 1 |
| Claw-Free | No | Minimum Dominating Set | 5 |
| Clique Number | 2 | Number of Components | 1 |
| Connected | Yes | Number of Edges | 10 |
| Density | 0.182 | Number of Triangles | 0 |
| Diameter | 8 | Number of Vertices | 11 |
| Edge Connectivity | 1 | Planar | Yes |
| Eulerian | No | Radius | 4 |
| Genus | 0 | Regular | No |
| Girth | undefined | Second Largest Eigenvalue | 1.71 |
| Hamiltonian | No | Smallest Eigenvalue | -2.122 |
| Independence Number | 6 | Vertex Connectivity | 1 |
A table row rendered like this indicates that the graph is marked as being interesting for that invariant.
Comments
Posted by Kevin Ryde at Nov 29, 2018 7:43 AM.
Each vertex is a partition of N=6, ie. a set of integers which sum to 6. There are 11 such. Each edge is from a partition to its successor under the Bulgarian solitaire rule: subtract 1 from each element, sum those 1s as a new term, discard any zeros.
N=6 is a triangular number and the steps form a tree ending at partition 1+2+3 which is unchanged by the solitaire rule and can be reckoned the tree root. This is the leaf nearest the centre.
N=6 is a triangular number and the steps form a tree ending at partition 1+2+3 which is unchanged by the solitaire rule and can be reckoned the tree root. This is the leaf nearest the centre.
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