Graph details

Graph # 33710

Adjacency matrix

000001100001
000010100011
000100001101
001010000011
010100000011
100000110100
110001010000
000001101100
001000010110
001001011000
010110001000
111110000000

Adjacency list

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

HoG graph id

33710

Graph name

n/a

Graph submitted by

Gunnar Brinkmann

Invariant values

The definitions of the invariants can be found here.
Invariant Value Invariant Value
Acyclic No Index 4.043
Algebraic Connectivity 1.16 Laplacian Largest Eigenvalue 6.782
Average Degree 4 Longest Induced Cycle 7
Bipartite No Longest Induced Path 7
Chromatic Index 5 Matching Number 6
Chromatic Number 3 Maximum Degree 5
Circumference 12 Minimum Degree 3
Claw-Free No Minimum Dominating Set 3
Clique Number 3 Number of Components 1
Connected Yes Number of Edges 24
Density 0.364 Number of Triangles 10
Diameter 3 Number of Vertices 12
Edge Connectivity 3 Planar Yes
Eulerian No Radius 3
Genus 0 Regular No
Girth 3 Second Largest Eigenvalue 2.861
Hamiltonian Yes Smallest Eigenvalue -2.529
Independence Number 4 Vertex Connectivity 3

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

Comments

Posted by Gunnar Brinkmann at May 28, 2019 5:29 PM.
ham_pol_min_1cut -- the unique polyhedron with one 3-cut and minimum number of hamiltonian cycles on this number of vertices

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