Graph details

Graph # 33545

Adjacency matrix

[Too large to display]

Adjacency list

[Too large to display]

HoG graph id

33545

Graph name

Binomial Tree Order 7

Graph submitted by

Kevin Ryde

Invariant values

The definitions of the invariants can be found here.
Invariant Value Invariant Value
Acyclic Yes Index 3.453
Algebraic Connectivity 0.014 Laplacian Largest Eigenvalue 9.314
Average Degree 1.984 Longest Induced Cycle undefined
Bipartite Yes Longest Induced Path 13
Chromatic Index 7 Matching Number 64
Chromatic Number Computation time out Maximum Degree 7
Circumference undefined Minimum Degree 1
Claw-Free No Minimum Dominating Set 64
Clique Number 2 Number of Components 1
Connected Yes Number of Edges 127
Density 0.016 Number of Triangles 0
Diameter 13 Number of Vertices 128
Edge Connectivity 1 Planar Yes
Eulerian No Radius 7
Genus 0 Regular No
Girth undefined Second Largest Eigenvalue 3.02
Hamiltonian No Smallest Eigenvalue -3.453
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.

Comments

Posted by Kevin Ryde at Feb 9, 2019 6:23 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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