Graph details

Graph # 33615

Adjacency matrix

00000000001000
00000100000000
00000010000000
00000001000000
00000000100000
01000000000001
00100000000001
00010000000100
00001000000010
00000000000111
10000000000110
00000001011000
00000000111000
00000110010000

Adjacency list

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

HoG graph id

33615

Graph name

Binary Tree Rotate Right-Arm 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 2.503
Algebraic Connectivity 0.15 Laplacian Largest Eigenvalue 5.369
Average Degree 2 Longest Induced Cycle 4
Bipartite Yes Longest Induced Path 6
Chromatic Index 3 Matching Number 6
Chromatic Number 2 Maximum Degree 3
Circumference 4 Minimum Degree 1
Claw-Free No Minimum Dominating Set 6
Clique Number 2 Number of Components 1
Connected Yes Number of Edges 14
Density 0.154 Number of Triangles 0
Diameter 6 Number of Vertices 14
Edge Connectivity 1 Planar Yes
Eulerian No Radius 3
Genus 0 Regular No
Girth 4 Second Largest Eigenvalue 1.801
Hamiltonian No Smallest Eigenvalue -2.503
Independence Number 8 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 2:10 AM.
Each graph vertex represents a binary tree of N=4 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.

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