Graph details

Graph # 27044

Adjacency matrix

[Too large to display]

Adjacency list

[Too large to display]

HoG graph id

27044

Graph name

twin alternate area tree level 5

Graph submitted by

Kevin Ryde

Invariant values

The definitions of the invariants can be found here.
Invariant Value Invariant Value
Acyclic Yes Index 2.231
Algebraic Connectivity 0.015 Laplacian Largest Eigenvalue 4.819
Average Degree 1.938 Longest Induced Cycle undefined
Bipartite Yes Longest Induced Path 23
Chromatic Index 3 Matching Number 16
Chromatic Number 2 Maximum Degree 3
Circumference undefined Minimum Degree 1
Claw-Free No Minimum Dominating Set 12
Clique Number 2 Number of Components 1
Connected Yes Number of Edges 31
Density 0.062 Number of Triangles 0
Diameter 23 Number of Vertices 32
Edge Connectivity 1 Planar Yes
Eulerian No Radius 12
Genus 0 Regular No
Girth undefined Second Largest Eigenvalue 2.141
Hamiltonian No Smallest Eigenvalue -2.231
Independence Number 16 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 26, 2017 5:33 AM.
Form a twin alternate curve by arranging four alternate paperfolding curves level 5 in a cycle (or two level 6 back-to-back). Graph vertices are the 2^5 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 23 is OEIS A053599.

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