Graph details

Graph # 33547

Adjacency matrix

01110000000000
10000000100010
10000000010001
10000000001100
00000001100010
00000001010001
00000001001100
00001110000000
01001000010000
00100100100000
00010010000001
00010010000010
01001000000100
00100100001000

Adjacency list

1: 2 3 4
2: 1 9 13
3: 1 10 14
4: 1 11 12
5: 8 9 13
6: 8 10 14
7: 8 11 12
8: 5 6 7
9: 2 5 10
10: 3 6 9
11: 4 7 14
12: 4 7 13
13: 2 5 12
14: 3 6 11

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).

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