Graph details

Graph # 33619

Adjacency matrix

[Too large to display]

Adjacency list

[Too large to display]

HoG graph id

33619

Graph name

Binary Tree Rotate Right-Arm 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 4.013
Algebraic Connectivity 0.045 Laplacian Largest Eigenvalue 8.769
Average Degree 2.5 Longest Induced Cycle 18
Bipartite Yes Longest Induced Path 26
Chromatic Index Computation time out Matching Number 57
Chromatic Number 2 Maximum Degree 5
Circumference Computation time out Minimum Degree 1
Claw-Free No Minimum Dominating Set 47
Clique Number 2 Number of Components 1
Connected Yes Number of Edges 165
Density 0.019 Number of Triangles 0
Diameter 10 Number of Vertices 132
Edge Connectivity 1 Planar Computation time out
Eulerian No Radius 5
Genus Computation time out Regular No
Girth 4 Second Largest Eigenvalue 3.391
Hamiltonian Computation time out Smallest Eigenvalue -4.013
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 23, 2019 2:14 AM.
Each graph vertex represents a binary tree of N=6 vertices. There are Catalan(6)=132 such. Each graph edge is a "rotate" of an edge on the right arm of the tree. (Or equivalently mirror image and rotate from/to the left arm.)

J. M. Pallo, "Right-Arm Rotation Distance Between Binary Trees", Information Processing Letters, volume 87, number 4, 2003, pages 173-177.

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