Graph details
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Adjacency matrix[Too large to display] |
Adjacency list[Too large to display] |
HoG graph id
32239
Graph name
Dudeney puzzle "Visiting the Towns"
Graph submitted by
Kevin Ryde
Invariant values
The definitions of the invariants can be found here.| Invariant | Value | Invariant | Value |
|---|---|---|---|
| Acyclic | No | Index | 3.071 |
| Algebraic Connectivity | 0.764 | Laplacian Largest Eigenvalue | 6.457 |
| Average Degree | 2.875 | Longest Induced Cycle | 10 |
| Bipartite | Yes | Longest Induced Path | 10 |
| Chromatic Index | 4 | Matching Number | 8 |
| Chromatic Number | 2 | Maximum Degree | 4 |
| Circumference | 16 | Minimum Degree | 2 |
| Claw-Free | No | Minimum Dominating Set | 4 |
| Clique Number | 2 | Number of Components | 1 |
| Connected | Yes | Number of Edges | 23 |
| Density | 0.192 | Number of Triangles | 0 |
| Diameter | 5 | Number of Vertices | 16 |
| Edge Connectivity | 2 | Planar | No |
| Eulerian | No | Radius | 4 |
| Genus | 1 | Regular | No |
| Girth | 4 | Second Largest Eigenvalue | 2.029 |
| Hamiltonian | Yes | Smallest Eigenvalue | -3.071 |
| Independence Number | 8 | 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 Nov 10, 2018 5:54 AM.
Dudeney gives this graph in a puzzle. Vertices are towns and edges are roads between them. The traveller is to visit each town once only, starting and ending at the same place, so a Hamiltonian cycle. Per Dudeney's solution, the degree-2 vertices force a unique Hamiltonian cycle.
Henry Ernest Dudeney, "Amusements in Mathematics", 1917, puzzle 243 "Visiting the Towns", pages 70, 198.
http://www.gutenberg.org/ebooks/16713
Henry Ernest Dudeney, "Amusements in Mathematics", 1917, puzzle 243 "Visiting the Towns", pages 70, 198.
http://www.gutenberg.org/ebooks/16713
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