Graph details

Graph # 33706

Adjacency matrix

00000110001
00010100101
00001010011
01001000101
00110000011
11000011000
10100101000
00000110110
01010001010
00101001100
11111000000

Adjacency list

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

HoG graph id

33706

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 4.044
Algebraic Connectivity 1.646 Laplacian Largest Eigenvalue 6.877
Average Degree 4 Longest Induced Cycle 6
Bipartite No Longest Induced Path 6
Chromatic Index 5 Matching Number 5
Chromatic Number 4 Maximum Degree 5
Circumference 11 Minimum Degree 3
Claw-Free No Minimum Dominating Set 2
Clique Number 3 Number of Components 1
Connected Yes Number of Edges 22
Density 0.4 Number of Triangles 8
Diameter 3 Number of Vertices 11
Edge Connectivity 3 Planar Yes
Eulerian No Radius 2
Genus 0 Regular No
Girth 3 Second Largest Eigenvalue 2.218
Hamiltonian Yes Smallest Eigenvalue -2.693
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 5:28 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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