Graph details

Graph # 44086

Adjacency matrix

011100011
101010110
110001101
100011011
010101111
001110111
011011011
110111101
101111110

Adjacency list

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

HoG graph id

44086

Graph name

Whythoff Game States, starting 3,2

Graph submitted by

Kevin Ryde

Invariant values

The definitions of the invariants can be found here.
Invariant Value Invariant Value
Acyclic No Index 5.879
Algebraic Connectivity 4.088 Laplacian Largest Eigenvalue 8.532
Average Degree 5.778 Longest Induced Cycle 5
Bipartite No Longest Induced Path 3
Chromatic Index 7 Matching Number 4
Chromatic Number 5 Maximum Degree 7
Circumference 9 Minimum Degree 5
Claw-Free Yes Minimum Dominating Set 2
Clique Number 5 Number of Components 1
Connected Yes Number of Edges 26
Density 0.722 Number of Triangles 29
Diameter 2 Number of Vertices 9
Edge Connectivity 5 Planar No
Eulerian No Radius 2
Genus 1 Regular No
Girth 3 Second Largest Eigenvalue 1.125
Hamiltonian Yes Smallest Eigenvalue -2.414
Independence Number 2 Vertex Connectivity 5

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

Comments

Posted by Kevin Ryde at Jan 10, 2021 4:58 AM.
The Whythoff game is played with two piles of tokens. A player takes any number from one pile, or the same number from both piles. The present graph is an example given by Michel Rigo http://hdl.handle.net/2268/100440 (page 13) where each vertex is a game state, the two piles are indistinguishable, starting from piles 3,2.

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