Graph details

Graph # 33712

Adjacency matrix

0000011000001
0000100011001
0001001000101
0010100000011
0101000000011
1000001001100
1010010000100
0000000011110
0100000101010
0100010110000
0010011100000
0001100110000
1111100000000

Adjacency list

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

HoG graph id

33712

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 4.039
Algebraic Connectivity 1.162 Laplacian Largest Eigenvalue 6.691
Average Degree 4 Longest Induced Cycle 8
Bipartite No Longest Induced Path 7
Chromatic Index 5 Matching Number 6
Chromatic Number 4 Maximum Degree 5
Circumference 13 Minimum Degree 3
Claw-Free No Minimum Dominating Set 3
Clique Number 3 Number of Components 1
Connected Yes Number of Edges 26
Density 0.333 Number of Triangles 10
Diameter 3 Number of Vertices 13
Edge Connectivity 3 Planar Yes
Eulerian No Radius 3
Genus 0 Regular No
Girth 3 Second Largest Eigenvalue 2.714
Hamiltonian Yes Smallest Eigenvalue -2.474
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 5:30 PM.
ham_pol_min_1cut -- one of the two polyhedra with one 3-cut and minimum number of hamiltonian cycles on this number of vertices

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