Graph details

Graph # 33611

Adjacency matrix

[Too large to display]

Adjacency list

[Too large to display]

HoG graph id


Graph name

Binary Tree Rotate A-Empty N=6

Graph submitted by

Kevin Ryde

Invariant values

The definitions of the invariants can be found here.
Invariant Value Invariant Value
Acyclic No Index 3.988
Algebraic Connectivity 0.018 Laplacian Largest Eigenvalue 8.548
Average Degree 3.182 Longest Induced Cycle Computation time out
Bipartite Yes Longest Induced Path Computation time out
Chromatic Index Computation time out Matching Number 66
Chromatic Number Computation time out Maximum Degree 5
Circumference Computation time out Minimum Degree 1
Claw-Free No Minimum Dominating Set Computation time out
Clique Number 2 Number of Components 1
Connected Yes Number of Edges 210
Density 0.024 Number of Triangles 0
Diameter 25 Number of Vertices 132
Edge Connectivity Computation time out Planar Computation time out
Eulerian No Radius 13
Genus Computation time out Regular No
Girth 4 Second Largest Eigenvalue 3.767
Hamiltonian Computation time out Smallest Eigenvalue -3.988
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.


Posted by Kevin Ryde at Feb 17, 2019 8:07 AM.
Each vertex represents a binary tree of N=6 vertices (there are Catalan(6)=132 such). Each edge is by a "rotate" where the first subtree of the rotate is empty. (Or equivalently where the end subtree is empty, that being the same by mirror image and rotate other way.) The result is edge intersection of Tamari (rotate) and Stanley (flip) lattices.

A. Bonnin and J.M. Pallo, "A Shortest Path Metric on Unlabelled Binary Trees", Pattern Recognition Letters, volume 13, 1992, pages 411-415.

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