Graph details

Graph # 35447

Adjacency matrix

[Too large to display]

Adjacency list

[Too large to display]

HoG graph id


Graph name

Binomial Both, order 4

Graph submitted by

Kevin Ryde

Invariant values

The definitions of the invariants can be found here.
Invariant Value Invariant Value
Acyclic No Index 2.935
Algebraic Connectivity 0.354 Laplacian Largest Eigenvalue 6.249
Average Degree 2.75 Longest Induced Cycle 8
Bipartite Yes Longest Induced Path 7
Chromatic Index 4 Matching Number 8
Chromatic Number 2 Maximum Degree 4
Circumference 8 Minimum Degree 2
Claw-Free No Minimum Dominating Set 4
Clique Number 2 Number of Components 1
Connected Yes Number of Edges 22
Density 0.183 Number of Triangles 0
Diameter 4 Number of Vertices 16
Edge Connectivity 2 Planar Yes
Eulerian No Radius 4
Genus 0 Regular No
Girth 4 Second Largest Eigenvalue 2.303
Hamiltonian No Smallest Eigenvalue -2.935
Independence Number 8 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 10:57 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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