Graph details

Graph # 33623

Adjacency matrix

[Too large to display]

Adjacency list

[Too large to display]

HoG graph id

33623

Graph name

Dexter 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 4.513
Algebraic Connectivity 0.54 Laplacian Largest Eigenvalue 9.804
Average Degree 4 Longest Induced Cycle 24
Bipartite No Longest Induced Path 25
Chromatic Index 7 Matching Number 21
Chromatic Number 3 Maximum Degree 7
Circumference 42 Minimum Degree 2
Claw-Free No Minimum Dominating Set 10
Clique Number 2 Number of Components 1
Connected Yes Number of Edges 84
Density 0.098 Number of Triangles 0
Diameter 7 Number of Vertices 42
Edge Connectivity 2 Planar No
Eulerian No Radius 4
Genus 4 Regular No
Girth 4 Second Largest Eigenvalue 3.259
Hamiltonian Yes Smallest Eigenvalue -4.448
Independence Number 20 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 2:27 AM.
Each graph vertex is a balanced binary string (Dyck word) of N pairs. There are Catalan(5)=42 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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