Graph details

Graph # 33704

Adjacency matrix

0000011001
0010100101
0101000101
0010001011
0100010101
1000101010
1001010010
0110100010
0001011100
1111100000

Adjacency list

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

HoG graph id

33704

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 4.048
Algebraic Connectivity 1.559 Laplacian Largest Eigenvalue 6.836
Average Degree 4 Longest Induced Cycle 6
Bipartite No Longest Induced Path 5
Chromatic Index 5 Matching Number 5
Chromatic Number 3 Maximum Degree 5
Circumference 10 Minimum Degree 3
Claw-Free No Minimum Dominating Set 2
Clique Number 3 Number of Components 1
Connected Yes Number of Edges 20
Density 0.444 Number of Triangles 8
Diameter 3 Number of Vertices 10
Edge Connectivity 3 Planar Yes
Eulerian No Radius 2
Genus 0 Regular No
Girth 3 Second Largest Eigenvalue 2.343
Hamiltonian Yes Smallest Eigenvalue -2.681
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 5:27 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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