Graph details

Graph # 33731

Adjacency matrix

000010101
000001011
000010011
000001101
101000110
010100110
100111001
011011001
111100110

Adjacency list

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

HoG graph id

33731

Graph name

Pappus Theorem Geometric Configuration

Graph submitted by

Kevin Ryde

Invariant values

The definitions of the invariants can be found here.
Invariant Value Invariant Value
Acyclic No Index 4.194
Algebraic Connectivity 2 Laplacian Largest Eigenvalue 7.732
Average Degree 4 Longest Induced Cycle 4
Bipartite No Longest Induced Path 4
Chromatic Index 6 Matching Number 4
Chromatic Number 3 Maximum Degree 6
Circumference 9 Minimum Degree 3
Claw-Free No Minimum Dominating Set 2
Clique Number 3 Number of Components 1
Connected Yes Number of Edges 18
Density 0.5 Number of Triangles 8
Diameter 2 Number of Vertices 9
Edge Connectivity 3 Planar Yes
Eulerian No Radius 2
Genus 0 Regular No
Girth 3 Second Largest Eigenvalue 1.414
Hamiltonian Yes Smallest Eigenvalue -2.78
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 Kevin Ryde at Jul 3, 2019 9:49 AM.
The Pappus theorem in geometry is 9 straight lines, with each line through 3 points. Here each graph vertex is a point and edges are between points adjacent geometrically on a line.

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