Graph details

Graph # 33561

Adjacency matrix

[Too large to display]

Adjacency list

[Too large to display]

HoG graph id


Graph name

Kreweras Lattice 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 8.023
Algebraic Connectivity 1.906 Laplacian Largest Eigenvalue 18.048
Average Degree 7.5 Longest Induced Cycle Computation time out
Bipartite Yes Longest Induced Path Computation time out
Chromatic Index 15 Matching Number 66
Chromatic Number Computation time out Maximum Degree 15
Circumference Computation time out Minimum Degree 5
Claw-Free No Minimum Dominating Set Computation time out
Clique Number 2 Number of Components 1
Connected Yes Number of Edges 495
Density 0.057 Number of Triangles 0
Diameter 5 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 5.224
Hamiltonian Computation time out Smallest Eigenvalue -8.023
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.


Posted by Kevin Ryde at Feb 9, 2019 8:20 AM.
Each graph vertex is one of the Catalan(6)=132 partitions of the integers 1..6 into non-crossing sets. Such a partition corresponds to an ordered rooted forest (its sets of siblings), and hence to a binary tree too.

Each graph edge is where one set in the partition splits into two to reach another partition (and hence is "graded" by number of sets in the partition).

G. Kreweras, "Sur les Partitions Non-Croisées d'Un Cycle", Discrete
Mathematics, volume 1, number 4, 1971, pages 333-350.

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