Graph details

Graph # 6607

Adjacency matrix

011110000
101001100
110000011
100011010
100100101
010100110
010011001
001101001
001010110

Adjacency list

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

HoG graph id

6607

Graph name

Paley graph on 9 vertices

Graph submitted by

Frédéric Vanhove

Invariant values

The definitions of the invariants can be found here.
Invariant Value Invariant Value
Acyclic No Index 4
Algebraic Connectivity 3 Laplacian Largest Eigenvalue 6
Average Degree 4 Longest Induced Cycle 6
Bipartite No Longest Induced Path 4
Chromatic Index 5 Matching Number 4
Chromatic Number 3 Maximum Degree 4
Circumference 9 Minimum Degree 4
Claw-Free Yes Minimum Dominating Set 3
Clique Number 3 Number of Components 1
Connected Yes Number of Edges 18
Density 0.5 Number of Triangles 6
Diameter 2 Number of Vertices 9
Edge Connectivity 4 Planar No
Eulerian Yes Radius 2
Genus 1 Regular Yes
Girth 3 Second Largest Eigenvalue 1
Hamiltonian Yes Smallest Eigenvalue -2
Independence Number 3 Vertex Connectivity 4

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

Comments

Posted by Frédéric Vanhove at Nov 26, 2012 12:07 PM.
Like all Paley graphs, it is strongly regular and self-complementary.

Posted by Jan Goedgebeur at Dec 12, 2014 5:49 PM.
This is also the line graph of K_{3,3}.

Posted by Kevin Ryde at Jun 23, 2015 1:05 AM.
Also a 3x3 square grid with wrap-around, ie. a torus. Edges are unit steps NSEW. Or edges by unit diagonal steps are the same. Or edges by knight moves 1,2 or 2,1 are the same (since 2 == -1 mod 3 so giving diagonals).

Posted by House of Graphs at Jan 29, 2019 9:24 AM.
A connected integral graph. A graph is called integral if all of its eigenvalues of its adjacency matrix are integral. See "Krzysztof T. ZwierzyƄski, Generating Integral Graphs Using PRACE Research Infrastructure" for more information.

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