Graph details
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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.
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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