# Graph details ### Adjacency matrix

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### Adjacency list

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33551

## Graph name

Tamari Lattice N=6

Kevin Ryde

## Invariant values

The definitions of the invariants can be found here.
Invariant Value Invariant Value
Acyclic No Index 5
Algebraic Connectivity 0.617 Laplacian Largest Eigenvalue 8.913
Average Degree 5 Longest Induced Cycle Computation time out
Bipartite No Longest Induced Path Computation time out
Chromatic Index Computation time out Matching Number 66
Chromatic Number 3 Maximum Degree 5
Circumference Computation time out Minimum Degree 5
Claw-Free No Minimum Dominating Set Computation time out
Clique Number 2 Number of Components 1
Connected Yes Number of Edges 330
Density 0.038 Number of Triangles 0
Diameter 7 Number of Vertices 132
Edge Connectivity Computation time out Planar Computation time out
Eulerian No Radius 5
Genus Computation time out Regular Yes
Girth 4 Second Largest Eigenvalue 4.383
Hamiltonian Computation time out Smallest Eigenvalue -3.913
Independence Number Computation time out 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 6:50 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=6 and there are Catalan(6) = 132 vertices.

Equivalently, binary tree rotation graph. Each vertex represents a binary tree of N=6 vertices and graph edges are between trees differing by one "rotation". Each tree edge can rotate, so degree N-1 regular (330 edges, OEIS A002054).

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