Graph details

Graph # 33621

Adjacency matrix

00001000000001
00010000000001
00000000010010
01000000000100
10000000010000
00000000100011
00000001100010
00000010001100
00000110000100
00101000001000
00000001010011
00010001100001
00100110001000
11000100001100

Adjacency list

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

HoG graph id

33621

Graph name

Dexter 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 3.316
Algebraic Connectivity 0.625 Laplacian Largest Eigenvalue 7.117
Average Degree 3 Longest Induced Cycle 9
Bipartite No Longest Induced Path 9
Chromatic Index 5 Matching Number 7
Chromatic Number 3 Maximum Degree 5
Circumference 13 Minimum Degree 2
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 5 Number of Vertices 14
Edge Connectivity 2 Planar Yes
Eulerian No Radius 3
Genus 0 Regular No
Girth 4 Second Largest Eigenvalue 1.992
Hamiltonian No Smallest Eigenvalue -3.288
Independence Number 7 Vertex Connectivity 2

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 2:25 AM.
Each graph vertex is a balanced binary string (Dyck word) of N pairs. There are Catalan(4)=14 such. Each graph edge is the "dexter" transform by Chapoton which shifts a block of 1s to raise their adjacent balanced substring. This is some multiple binary tree "rotates". Chapoton notes right-arm rotates are a subset of dexter.

F. Chapoton, "Some Properties of a New Partial Order on Dyck Paths", September 2018.
https://hal.archives-ouvertes.fr/hal-01878792
https://arxiv.org/abs/1809.10981

You need to be logged in to be able to add comments.