Graph details

Graph # 35457

Adjacency matrix

011100000011000
100000001100011
100000100101001
100000011010100
000001100110100
000010011011000
001010010000011
000101100000110
010101000001001
011010000000110
100111000000011
101001001000110
000110010101001
010000110111000
011000101010100

Adjacency list

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

HoG graph id

35457

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 5.372
Algebraic Connectivity 3.166 Laplacian Largest Eigenvalue 9.012
Average Degree 5.333 Longest Induced Cycle 7
Bipartite No Longest Induced Path 6
Chromatic Index 6 Matching Number 7
Chromatic Number 4 Maximum Degree 6
Circumference 15 Minimum Degree 5
Claw-Free No Minimum Dominating Set 3
Clique Number 3 Number of Components 1
Connected Yes Number of Edges 40
Density 0.381 Number of Triangles 10
Diameter 2 Number of Vertices 15
Edge Connectivity 5 Planar No
Eulerian No Radius 2
Genus 3 Regular No
Girth 3 Second Largest Eigenvalue 1.945
Hamiltonian Yes Smallest Eigenvalue -3.327
Independence Number 4 Vertex Connectivity 5

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 16, 2020 2:31 PM.
Extremal Ramsey graph containing no K4-e as a subgraph, nor a K5 in the complement. Has the fewest number of edges among all such graphs.

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