Graph details

Graph # 33543

Adjacency matrix

[Too large to display]

Adjacency list

[Too large to display]

HoG graph id


Graph name

Binomial Tree Order 6

Graph submitted by

Kevin Ryde

Invariant values

The definitions of the invariants can be found here.
Invariant Value Invariant Value
Acyclic Yes Index 3.163
Algebraic Connectivity 0.028 Laplacian Largest Eigenvalue 8.194
Average Degree 1.969 Longest Induced Cycle undefined
Bipartite Yes Longest Induced Path 11
Chromatic Index 6 Matching Number 32
Chromatic Number Computation time out Maximum Degree 6
Circumference undefined Minimum Degree 1
Claw-Free No Minimum Dominating Set 32
Clique Number 2 Number of Components 1
Connected Yes Number of Edges 63
Density 0.031 Number of Triangles 0
Diameter 11 Number of Vertices 64
Edge Connectivity 1 Planar Yes
Eulerian No Radius 6
Genus 0 Regular No
Girth undefined Second Largest Eigenvalue 2.689
Hamiltonian No Smallest Eigenvalue -3.163
Independence Number Computation time out Vertex Connectivity 1

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 6:22 AM.
An order N binomial tree has a root vertex and under it N sub-trees which are binomial trees orders 0 to N-1 inclusive. An order 0 tree is a single vertex. The number of vertices at depth d is binomial(N,d).

Equivalently, an order N tree is integers n=0 to n=2^N-1 inclusive with root n=0 and parent of n is n with its least significant 1-bit cleared to 0.

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