Graph details

Graph # 32269

Adjacency matrix

0000000001
0000000001
0000000010
0000000010
0000000100
0000000100
0000000011
0000110001
0011001000
1100001100

Adjacency list

1: 10
2: 10
3: 9
4: 9
5: 8
6: 8
7: 9 10
8: 5 6 10
9: 3 4 7
10: 1 2 7 8

HoG graph id

32269

Graph name

Tree Automorphisms E8, N=10

Graph submitted by

Kevin Ryde

Invariant values

The definitions of the invariants can be found here.
Invariant Value Invariant Value
Acyclic Yes Index 2.262
Algebraic Connectivity 0.18 Laplacian Largest Eigenvalue 5.346
Average Degree 1.8 Longest Induced Cycle undefined
Bipartite Yes Longest Induced Path 5
Chromatic Index 4 Matching Number 3
Chromatic Number 2 Maximum Degree 4
Circumference undefined Minimum Degree 1
Claw-Free No Minimum Dominating Set 3
Clique Number 2 Number of Components 1
Connected Yes Number of Edges 9
Density 0.2 Number of Triangles 0
Diameter 5 Number of Vertices 10
Edge Connectivity 1 Planar Yes
Eulerian No Radius 3
Genus 0 Regular No
Girth undefined Second Largest Eigenvalue 1.657
Hamiltonian No Smallest Eigenvalue -2.262
Independence Number 7 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 Dec 15, 2018 6:41 AM.
This tree has automorphism group E8 = C2xC2xC2. Its n=10 vertices is the fewest for trees of this group. It is one of two such n=10. This one has 4 fixed vertices (the non-leaves).

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