Graph details

Graph # 32274

Adjacency matrix

000000001
000000100
000000010
000010001
000100001
000000111
010001011
001001101
100111110

Adjacency list

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

HoG graph id

32274

Graph name

Lex-Max Vpar Forests Differences N=4

Graph submitted by

Kevin Ryde

Invariant values

The definitions of the invariants can be found here.
Invariant Value Invariant Value
Acyclic No Index 3.465
Algebraic Connectivity 0.636 Laplacian Largest Eigenvalue 7.073
Average Degree 2.667 Longest Induced Cycle 3
Bipartite No Longest Induced Path 3
Chromatic Index 6 Matching Number 4
Chromatic Number 4 Maximum Degree 6
Circumference 4 Minimum Degree 1
Claw-Free No Minimum Dominating Set 3
Clique Number 4 Number of Components 1
Connected Yes Number of Edges 12
Density 0.333 Number of Triangles 5
Diameter 3 Number of Vertices 9
Edge Connectivity 1 Planar Yes
Eulerian No Radius 2
Genus 0 Regular No
Girth 3 Second Largest Eigenvalue 1.51
Hamiltonian No Smallest Eigenvalue -2
Independence Number 5 Vertex Connectivity 1

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

Comments

Posted by Kevin Ryde at Dec 16, 2018 2:35 AM.
Each graph vertex is an unlabelled rooted forest of n=4 vertices (9 of them) represented by a labelled rooted forest in vertex parent array form (vpar). Labelling is chosen to give each the lexicographically greatest vpar array. Graph edges are between arrays differing in one position.

The 3 degree-1 vertices are vpar=[0,0,0,0] singletons, vpar=[4,3,1,0] path-4, and vpar=[4,4,0,3] star-4. The latter has the degree-6 neighbour. The clique-4 is vpar=[4,X,0,0] with X=0,1,3,4.

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