# Graph details ### Adjacency matrix

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### Adjacency list

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33549

## Graph name

Tamari Lattice N=5

Kevin Ryde

## Invariant values

The definitions of the invariants can be found here.
Invariant Value Invariant Value
Acyclic No Index 4
Algebraic Connectivity 0.768 Laplacian Largest Eigenvalue 7.177
Average Degree 4 Longest Induced Cycle 23
Bipartite No Longest Induced Path 23
Chromatic Index Computation time out Matching Number 21
Chromatic Number 3 Maximum Degree 4
Circumference 42 Minimum Degree 4
Claw-Free No Minimum Dominating Set 10
Clique Number 2 Number of Components 1
Connected Yes Number of Edges 84
Density 0.098 Number of Triangles 0
Diameter 5 Number of Vertices 42
Edge Connectivity 4 Planar Computation time out
Eulerian Yes Radius 4
Genus Computation time out Regular Yes
Girth 4 Second Largest Eigenvalue 3.232
Hamiltonian Yes Smallest Eigenvalue -3.177
Independence Number 16 Vertex Connectivity Computation time out

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 6:48 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=5 and there are Catalan(5) = 42 vertices.

Equivalently, binary tree rotation graph. Each vertex represents a binary tree of N=5 vertices and graph edges are between trees differing by one "rotation". Each tree edge can rotate, so degree N-1 regular (84 edges, OEIS A002054).

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