Graph details
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Adjacency matrix
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Adjacency list
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HoG graph id
33547
Graph name
Tamari Lattice N=4
Graph submitted by
Kevin Ryde
Invariant values
The definitions of the invariants can be found here.| Invariant | Value | Invariant | Value |
|---|---|---|---|
| Acyclic | No | Index | 3 |
| Algebraic Connectivity | 1 | Laplacian Largest Eigenvalue | 5.414 |
| Average Degree | 3 | Longest Induced Cycle | 9 |
| Bipartite | No | Longest Induced Path | 8 |
| Chromatic Index | 3 | Matching Number | 7 |
| Chromatic Number | 3 | Maximum Degree | 3 |
| Circumference | 14 | Minimum Degree | 3 |
| Claw-Free | No | Minimum Dominating Set | 4 |
| Clique Number | 2 | Number of Components | 1 |
| Connected | Yes | Number of Edges | 21 |
| Density | 0.231 | Number of Triangles | 0 |
| Diameter | 4 | Number of Vertices | 14 |
| Edge Connectivity | 3 | Planar | Yes |
| Eulerian | No | Radius | 3 |
| Genus | 0 | Regular | Yes |
| Girth | 4 | Second Largest Eigenvalue | 2 |
| Hamiltonian | Yes | Smallest Eigenvalue | -2.414 |
| Independence Number | 6 | Vertex Connectivity | 3 |
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 9, 2019 6:44 AM.
The Tamari lattice by Dov Tamari has graph vertices as parenthesizations of N+1 objects into pairs, and graph edges between those differing by one application of the associative law. Hence also called an associahedron. Here N=4 and there are Catalan(4) = 14 vertices.
Equivalently, binary tree rotation graph. Each vertex represents a binary tree of N=4 vertices and graph edges are between trees differing by one "rotation". Each tree edge can rotate, so degree N-1 regular (21 edges, OEIS A002054).
Equivalently, binary tree rotation graph. Each vertex represents a binary tree of N=4 vertices and graph edges are between trees differing by one "rotation". Each tree edge can rotate, so degree N-1 regular (21 edges, OEIS A002054).
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