Graph details

Graph # 33625

Adjacency matrix

[Too large to display]

Adjacency list

[Too large to display]

HoG graph id

33625

Graph name

Dexter 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 5.718
Algebraic Connectivity 0.491 Laplacian Largest Eigenvalue 12.514
Average Degree 5 Longest Induced Cycle Computation time out
Bipartite No Longest Induced Path Computation time out
Chromatic Index 9 Matching Number 66
Chromatic Number Computation time out Maximum Degree 9
Circumference Computation time out Minimum Degree 3
Claw-Free No Minimum Dominating Set Computation time out
Clique Number 2 Number of Components 1
Connected Yes Number of Edges 330
Density 0.038 Number of Triangles 0
Diameter 9 Number of Vertices 132
Edge Connectivity Computation time out Planar Computation time out
Eulerian No Radius 5
Genus Computation time out Regular No
Girth 4 Second Largest Eigenvalue 4.505
Hamiltonian Computation time out Smallest Eigenvalue -5.611
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 2:28 AM.
Each graph vertex is a balanced binary string (Dyck word) of N pairs. There are Catalan(6)=132 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

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