Graph details

Graph # 27042

Adjacency matrix

[Too large to display]

Adjacency list

[Too large to display]

HoG graph id


Graph name

twin alternate area tree level 4

Graph submitted by

Kevin Ryde

Invariant values

The definitions of the invariants can be found here.
Invariant Value Invariant Value
Acyclic Yes Index 2.146
Algebraic Connectivity 0.05 Laplacian Largest Eigenvalue 4.71
Average Degree 1.875 Longest Induced Cycle undefined
Bipartite Yes Longest Induced Path 13
Chromatic Index 3 Matching Number 8
Chromatic Number 2 Maximum Degree 3
Circumference undefined Minimum Degree 1
Claw-Free No Minimum Dominating Set 6
Clique Number 2 Number of Components 1
Connected Yes Number of Edges 15
Density 0.125 Number of Triangles 0
Diameter 13 Number of Vertices 16
Edge Connectivity 1 Planar Yes
Eulerian No Radius 7
Genus 0 Regular No
Girth undefined Second Largest Eigenvalue 1.835
Hamiltonian No Smallest Eigenvalue -2.146
Independence Number 8 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 5:23 AM.
Form a twin alternate curve by arranging four alternate paperfolding curves level 4 in a cycle (or two level 5 back-to-back). Graph vertices are the 2^4 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.

This is the first twin alternate area tree level which is not just a path. Diameter 13 is OEIS A053599.

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