Graph details

Graph # 33633

Adjacency matrix

000110000000
000001010000
000000101000
100000000101
100000000011
010000000011
001000000011
010000000101
001000000101
000100011000
000011100000
000111111000

Adjacency list

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

HoG graph id

33633

Graph name

Grätzer Example Lattice

Graph submitted by

Kevin Ryde

Invariant values

The definitions of the invariants can be found here.
Invariant Value Invariant Value
Acyclic No Index 3.317
Algebraic Connectivity 1 Laplacian Largest Eigenvalue 7.646
Average Degree 3 Longest Induced Cycle 8
Bipartite Yes Longest Induced Path 8
Chromatic Index 6 Matching Number 6
Chromatic Number 2 Maximum Degree 6
Circumference 12 Minimum Degree 2
Claw-Free No Minimum Dominating Set 4
Clique Number 2 Number of Components 1
Connected Yes Number of Edges 18
Density 0.273 Number of Triangles 0
Diameter 4 Number of Vertices 12
Edge Connectivity 2 Planar No
Eulerian No Radius 2
Genus 1 Regular No
Girth 4 Second Largest Eigenvalue 1.732
Hamiltonian Yes Smallest Eigenvalue -3.317
Independence Number 6 Vertex Connectivity 2

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

Comments

Posted by Kevin Ryde at Mar 17, 2019 1:02 AM.
Appears in George Grätzer, "General Lattice Theory", second edition, exercise 15, figure 4, pages 16-17, with minimum and maximum as the degree-3s distance 4 apart. The exercise asks whether it is a lattice (yes).

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