Graph details

Graph # 33617

Adjacency matrix

[Too large to display]

Adjacency list

[Too large to display]

HoG graph id

33617

Graph name

Binary Tree Rotate Right-Arm N=5

Graph submitted by

Kevin Ryde

Invariant values

The definitions of the invariants can be found here.
Invariant Value Invariant Value
Acyclic No Index 3.255
Algebraic Connectivity 0.075 Laplacian Largest Eigenvalue 7.055
Average Degree 2.286 Longest Induced Cycle 4
Bipartite Yes Longest Induced Path 12
Chromatic Index 4 Matching Number 18
Chromatic Number 2 Maximum Degree 4
Circumference 16 Minimum Degree 1
Claw-Free No Minimum Dominating Set 15
Clique Number 2 Number of Components 1
Connected Yes Number of Edges 48
Density 0.056 Number of Triangles 0
Diameter 8 Number of Vertices 42
Edge Connectivity 1 Planar Yes
Eulerian No Radius 4
Genus 0 Regular No
Girth 4 Second Largest Eigenvalue 2.611
Hamiltonian No Smallest Eigenvalue -3.255
Independence Number 24 Vertex Connectivity 1

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 2:13 AM.
Each graph vertex represents a binary tree of N=5 vertices. There are Catalan(4)=14 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.

Rik Sengupta and Warut Suksompong, "The Comb Poset and the Parsewords Function". The present graph is figure 11.
http://www-users.math.umn.edu/~reiner/REU/SenguptaSuksompong2010.pdf

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