Graph details

Graph # 27046

Adjacency matrix

[Too large to display]

Adjacency list

[Too large to display]

HoG graph id


Graph name

twin alternate area tree level 6

Graph submitted by

Kevin Ryde

Invariant values

The definitions of the invariants can be found here.
Invariant Value Invariant Value
Acyclic Yes Index 2.368
Algebraic Connectivity 0.005 Laplacian Largest Eigenvalue 5.15
Average Degree 1.969 Longest Induced Cycle undefined
Bipartite Yes Longest Induced Path 37
Chromatic Index 3 Matching Number 32
Chromatic Number 2 Maximum Degree 3
Circumference undefined Minimum Degree 1
Claw-Free No Minimum Dominating Set 24
Clique Number 2 Number of Components 1
Connected Yes Number of Edges 63
Density 0.031 Number of Triangles 0
Diameter 37 Number of Vertices 64
Edge Connectivity 1 Planar Yes
Eulerian No Radius 19
Genus 0 Regular No
Girth undefined Second Largest Eigenvalue 2.226
Hamiltonian No Smallest Eigenvalue -2.368
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 26, 2017 5:54 AM.
Form a twin alternate curve by arranging four alternate paperfolding curves level 6 in a cycle (or two level 7 back-to-back). Graph vertices are the 2^6 unit squares inside. Edges connect squares beside consecutive curve segments, or equivalently if the curve is drawn with corners chamfered off leaving little gaps at corners then squares are connected through those gaps.

Diameter 37 is OEIS A053599.

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