Graph details

Graph # 33714

Adjacency matrix

0000011000001
0000010001011
0000100010011
0000101000101
0011000000101
1100001001000
1001010001000
0000000011110
0010000100110
0100011100000
0001100110000
0110000110000
1111100000000

Adjacency list

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

HoG graph id

33714

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 4.037
Algebraic Connectivity 1.128 Laplacian Largest Eigenvalue 6.986
Average Degree 4 Longest Induced Cycle 7
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 9
Diameter 3 Number of Vertices 13
Edge Connectivity 3 Planar Yes
Eulerian No Radius 3
Genus 0 Regular No
Girth 3 Second Largest Eigenvalue 2.735
Hamiltonian Yes Smallest Eigenvalue -2.726
Independence Number 5 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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