Graph details

Graph # 33640

Adjacency matrix

[Too large to display]

Adjacency list

[Too large to display]

HoG graph id

33640

Graph name

Fibonacci Lattice to N=6

Graph submitted by

Kevin Ryde

Invariant values

The definitions of the invariants can be found here.
Invariant Value Invariant Value
Acyclic No Index 4.253
Algebraic Connectivity 0.267 Laplacian Largest Eigenvalue 9.431
Average Degree 3.515 Longest Induced Cycle 14
Bipartite Yes Longest Induced Path 18
Chromatic Index 7 Matching Number 12
Chromatic Number 2 Maximum Degree 7
Circumference 24 Minimum Degree 1
Claw-Free No Minimum Dominating Set 7
Clique Number 2 Number of Components 1
Connected Yes Number of Edges 58
Density 0.11 Number of Triangles 0
Diameter 6 Number of Vertices 33
Edge Connectivity 1 Planar No
Eulerian No Radius 3
Genus 2 Regular No
Girth 4 Second Largest Eigenvalue 3.182
Hamiltonian No Smallest Eigenvalue -4.253
Independence Number 21 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 Mar 17, 2019 1:19 AM.
Per Stanley, each vertex is a list of 1s and 2s with sum <= 6. There are Fibonacci(N+3)-1 = 33 such. Edges are by increasing one term 1->2 or append a new 1 to reach another list. The number of vertices with sum=k is Fibonacci(k+1).

Richard P. Stanley, "The Fibonacci Lattice", Fibonacci Quarterly, volume 13, number 3, October 1975, pages 215-232. The present graph is F1 page 227.
https://fq.math.ca/13-3.html
https://fq.math.ca/Scanned/13-3/stanley.pdf

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