Graph details

Graph # 33718

Adjacency matrix

000001100000001
000010000001011
000100100000101
001010000000011
010100000000011
100000100010100
101001000000100
000000001101010
000000010110100
000000011011000
000001001101000
010000010110000
001001101000000
010110010000000
111110000000000

Adjacency list

1: 6 7 15
2: 5 12 14 15
3: 4 7 13 15
4: 3 5 14 15
5: 2 4 14 15
6: 1 7 11 13
7: 1 3 6 13
8: 9 10 12 14
9: 8 10 11 13
10: 8 9 11 12
11: 6 9 10 12
12: 2 8 10 11
13: 3 6 7 9
14: 2 4 5 8
15: 1 2 3 4 5

HoG graph id

33718

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 4.035
Algebraic Connectivity 0.914 Laplacian Largest Eigenvalue 6.914
Average Degree 4 Longest Induced Cycle 9
Bipartite No Longest Induced Path 8
Chromatic Index 5 Matching Number 7
Chromatic Number 3 Maximum Degree 5
Circumference 15 Minimum Degree 3
Claw-Free No Minimum Dominating Set 3
Clique Number 3 Number of Components 1
Connected Yes Number of Edges 30
Density 0.286 Number of Triangles 12
Diameter 4 Number of Vertices 15
Edge Connectivity 3 Planar Yes
Eulerian No Radius 3
Genus 0 Regular No
Girth 3 Second Largest Eigenvalue 3.158
Hamiltonian Yes Smallest Eigenvalue -2.827
Independence Number 6 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 5:32 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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