Graph details

Graph # 33555

Adjacency matrix

000000000100
000000000001
000000000001
000000000010
000001000000
000010100000
000001000100
000000001001
000000010010
100000100010
000100001100
011000010000

Adjacency list

1: 10
2: 12
3: 12
4: 11
5: 6
6: 5 7
7: 6 10
8: 9 12
9: 8 11
10: 1 7 11
11: 4 9 10
12: 2 3 8

HoG graph id

33555

Graph name

Seidel Cospectral Tree N=12

Graph submitted by

Kevin Ryde

Invariant values

The definitions of the invariants can be found here.
Invariant Value Invariant Value
Acyclic Yes Index 2.147
Algebraic Connectivity 0.099 Laplacian Largest Eigenvalue 4.715
Average Degree 1.833 Longest Induced Cycle undefined
Bipartite Yes Longest Induced Path 8
Chromatic Index 3 Matching Number 5
Chromatic Number 2 Maximum Degree 3
Circumference undefined Minimum Degree 1
Claw-Free No Minimum Dominating Set 4
Clique Number 2 Number of Components 1
Connected Yes Number of Edges 11
Density 0.167 Number of Triangles 0
Diameter 8 Number of Vertices 12
Edge Connectivity 1 Planar Yes
Eulerian No Radius 4
Genus 0 Regular No
Girth undefined Second Largest Eigenvalue 1.82
Hamiltonian No Smallest Eigenvalue -2.147
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 Feb 9, 2019 7:08 AM.
This tree has its Seidel adjacency matrix cospectral with another n=12 tree. N=12 is the fewest vertices where Seidel cospectral trees occur and this pair is the only such n=12. This tree is unicentroidal and its partner is bicentroidal.

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