Graph details

Graph # 35449

Adjacency matrix

[Too large to display]

Adjacency list

[Too large to display]

HoG graph id


Graph name

Binomial Both, order 5

Graph submitted by

Kevin Ryde

Invariant values

The definitions of the invariants can be found here.
Invariant Value Invariant Value
Acyclic No Index 3.217
Algebraic Connectivity 0.171 Laplacian Largest Eigenvalue 7.239
Average Degree 2.875 Longest Induced Cycle 10
Bipartite Yes Longest Induced Path 11
Chromatic Index 5 Matching Number 16
Chromatic Number 2 Maximum Degree 5
Circumference 10 Minimum Degree 2
Claw-Free No Minimum Dominating Set 8
Clique Number 2 Number of Components 1
Connected Yes Number of Edges 46
Density 0.093 Number of Triangles 0
Diameter 5 Number of Vertices 32
Edge Connectivity 2 Planar Yes
Eulerian No Radius 5
Genus 0 Regular No
Girth 4 Second Largest Eigenvalue 2.759
Hamiltonian No Smallest Eigenvalue -3.217
Independence Number 16 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 10:59 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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