Graph details

Graph # 35451

Adjacency matrix

[Too large to display]

Adjacency list

[Too large to display]

HoG graph id


Graph name

Binomial Both, order 6

Graph submitted by

Kevin Ryde

Invariant values

The definitions of the invariants can be found here.
Invariant Value Invariant Value
Acyclic No Index 3.452
Algebraic Connectivity 0.084 Laplacian Largest Eigenvalue 8.277
Average Degree 2.938 Longest Induced Cycle 12
Bipartite Yes Longest Induced Path 16
Chromatic Index 6 Matching Number 32
Chromatic Number Computation time out Maximum Degree 6
Circumference 12 Minimum Degree 2
Claw-Free No Minimum Dominating Set 16
Clique Number 2 Number of Components 1
Connected Yes Number of Edges 94
Density 0.047 Number of Triangles 0
Diameter 6 Number of Vertices 64
Edge Connectivity 2 Planar Computation time out
Eulerian No Radius 6
Genus Computation time out Regular No
Girth 4 Second Largest Eigenvalue 3.082
Hamiltonian No Smallest Eigenvalue -3.452
Independence Number 32 Vertex Connectivity 2

A table row rendered like this indicates that the graph is marked as being interesting for that invariant.


Posted by Kevin Ryde at Jun 14, 2020 11:01 AM.
A "binomial both" order k is a binomial tree order k both up and down. Each vertex is an integer 0 to 2^k-1 written with k many bits. Each v>0 has an edge to v with its lowest 1-bit cleared (binomial tree parent). Each v<2^k-1 has an edge to v with its lowest 0-bit set to 1, which is a bit-flipped binomial tree. The result is a graded lattice.

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