Graph details

Graph # 32267

Adjacency matrix

00000000
00000000
00010000
00100000
00000010
00000001
00001001
00000110

Adjacency list

1:
2:
3: 4
4: 3
5: 7
6: 8
7: 5 8
8: 6 7

HoG graph id

32267

Graph name

Forest Automorphisms E8, N=8

Graph submitted by

Kevin Ryde

Invariant values

The definitions of the invariants can be found here.
Invariant Value Invariant Value
Acyclic Yes Index 1.618
Algebraic Connectivity 0 Laplacian Largest Eigenvalue 3.414
Average Degree 1 Longest Induced Cycle undefined
Bipartite Yes Longest Induced Path 3
Chromatic Index 2 Matching Number 3
Chromatic Number 2 Maximum Degree 2
Circumference undefined Minimum Degree 0
Claw-Free Yes Minimum Dominating Set 5
Clique Number 2 Number of Components 4
Connected No Number of Edges 4
Density 0.143 Number of Triangles 0
Diameter infinity Number of Vertices 8
Edge Connectivity 0 Planar Yes
Eulerian No Radius undefined
Genus undefined Regular No
Girth undefined Second Largest Eigenvalue 1
Hamiltonian No Smallest Eigenvalue -1.618
Independence Number 5 Vertex Connectivity 0

A table row rendered like this indicates that the graph is marked as being interesting for that invariant.

Comments

Posted by Kevin Ryde at Dec 15, 2018 6:36 AM.
This forest has automorphism group E8 = C2xC2xC2. Its n=8 vertices is the second fewest for a forest with this group, and it is the only such n=8.

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