Graph details

Graph # 45618

Adjacency matrix

010111100000001
100001111001001
000110011110001
101011000100111
101100100010111
110100010101101
110010001011011
011001001010111
011000110100111
001101001011011
001010110101101
010001100110111
000111011011001
000110111101001
111111111111110

Adjacency list

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

HoG graph id

45618

Graph name

n/a

Graph submitted by

Steven Van Overberghe

Invariant values

The definitions of the invariants can be found here.
Invariant Value Invariant Value
Acyclic No Index 8.419
Algebraic Connectivity 4.959 Laplacian Largest Eigenvalue 15
Average Degree 8.133 Longest Induced Cycle 6
Bipartite No Longest Induced Path 5
Chromatic Index 14 Matching Number 7
Chromatic Number 6 Maximum Degree 14
Circumference 15 Minimum Degree 6
Claw-Free No Minimum Dominating Set 1
Clique Number 4 Number of Components 1
Connected Yes Number of Edges 61
Density 0.581 Number of Triangles 85
Diameter 2 Number of Vertices 15
Edge Connectivity 6 Planar Computation time out
Eulerian No Radius 1
Genus Computation time out Regular No
Girth 3 Second Largest Eigenvalue 2.045
Hamiltonian Yes Smallest Eigenvalue -3.565
Independence Number 4 Vertex Connectivity 6

A table row rendered like this indicates that the graph is marked as being interesting for that invariant.

Comments

Posted by Steven Van Overberghe at Jun 18, 2021 9:05 PM.
Minimal (3,3;5)-edge-folkman graph. It is bicritical: adding any edge makes a K_5, removing any edge drops the arrowing property.

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