Grünbaum (Subscript[20, 4]) Graph

Author

Eric W. Weisstein
July 31, 2026

This notebook downloaded from https://mathworld.wolfram.com/notebooks/GraphTheory/Gruenbaum20-4Graph.nb.

For more information, see Eric's MathWorld entry https://mathworld.wolfram.com/Gruenbaum20-4Graph.html.

©2026 Wolfram Research, Inc. except for portions noted otherwise

Sources

Levi graph of the Grunbaum 20-4 configuration. Source: B. Grunbaum, Musings on an Example of Danzer's, European Journal of Combinatorics 29 (2008), 1910-1918, https://doi.org/10.1016/j.ejc.2008.01.004

Incidence data

incidence={{1,3,13,14},{1,4,10,9},{1,6,12,17},{1,7,11,20},{2,4,15,6},{2,5,12,11},{2,8,14,18},{2,9,13,16},{3,5,7,8},{3,10,6,19},{3,11,15,17},{4,13,7,18},{4,12,8,20},{5,15,9,19},{5,14,10,16},{6,11,18,16},{7,12,19,16},{8,13,19,17},{9,14,20,17},{10,15,20,18}}

Levi graph

edges={"Point 1"\[UndirectedEdge]"Line 1","Point 3"\[UndirectedEdge]"Line 1","Point 13"\[UndirectedEdge]"Line 1","Point 14"\[UndirectedEdge]"Line 1","Point 1"\[UndirectedEdge]"Line 2","Point 4"\[UndirectedEdge]"Line 2","Point 10"\[UndirectedEdge]"Line 2","Point 9"\[UndirectedEdge]"Line 2","Point 1"\[UndirectedEdge]"Line 3","Point 6"\[UndirectedEdge]"Line 3","Point 12"\[UndirectedEdge]"Line 3","Point 17"\[UndirectedEdge]"Line 3","Point 1"\[UndirectedEdge]"Line 4","Point 7"\[UndirectedEdge]"Line 4","Point 11"\[UndirectedEdge]"Line 4","Point 20"\[UndirectedEdge]"Line 4","Point 2"\[UndirectedEdge]"Line 5","Point 4"\[UndirectedEdge]"Line 5","Point 15"\[UndirectedEdge]"Line 5","Point 6"\[UndirectedEdge]"Line 5","Point 2"\[UndirectedEdge]"Line 6","Point 5"\[UndirectedEdge]"Line 6","Point 12"\[UndirectedEdge]"Line 6","Point 11"\[UndirectedEdge]"Line 6","Point 2"\[UndirectedEdge]"Line 7","Point 8"\[UndirectedEdge]"Line 7","Point 14"\[UndirectedEdge]"Line 7","Point 18"\[UndirectedEdge]"Line 7","Point 2"\[UndirectedEdge]"Line 8","Point 9"\[UndirectedEdge]"Line 8","Point 13"\[UndirectedEdge]"Line 8","Point 16"\[UndirectedEdge]"Line 8","Point 3"\[UndirectedEdge]"Line 9","Point 5"\[UndirectedEdge]"Line 9","Point 7"\[UndirectedEdge]"Line 9","Point 8"\[UndirectedEdge]"Line 9","Point 3"\[UndirectedEdge]"Line 10","Point 10"\[UndirectedEdge]"Line 10","Point 6"\[UndirectedEdge]"Line 10","Point 19"\[UndirectedEdge]"Line 10","Point 3"\[UndirectedEdge]"Line 11","Point 11"\[UndirectedEdge]"Line 11","Point 15"\[UndirectedEdge]"Line 11","Point 17"\[UndirectedEdge]"Line 11","Point 4"\[UndirectedEdge]"Line 12","Point 13"\[UndirectedEdge]"Line 12","Point 7"\[UndirectedEdge]"Line 12","Point 18"\[UndirectedEdge]"Line 12","Point 4"\[UndirectedEdge]"Line 13","Point 12"\[UndirectedEdge]"Line 13","Point 8"\[UndirectedEdge]"Line 13","Point 20"\[UndirectedEdge]"Line 13","Point 5"\[UndirectedEdge]"Line 14","Point 15"\[UndirectedEdge]"Line 14","Point 9"\[UndirectedEdge]"Line 14","Point 19"\[UndirectedEdge]"Line 14","Point 5"\[UndirectedEdge]"Line 15","Point 14"\[UndirectedEdge]"Line 15","Point 10"\[UndirectedEdge]"Line 15","Point 16"\[UndirectedEdge]"Line 15","Point 6"\[UndirectedEdge]"Line 16","Point 11"\[UndirectedEdge]"Line 16","Point 18"\[UndirectedEdge]"Line 16","Point 16"\[UndirectedEdge]"Line 16","Point 7"\[UndirectedEdge]"Line 17","Point 12"\[UndirectedEdge]"Line 17","Point 19"\[UndirectedEdge]"Line 17","Point 16"\[UndirectedEdge]"Line 17","Point 8"\[UndirectedEdge]"Line 18","Point 13"\[UndirectedEdge]"Line 18","Point 19"\[UndirectedEdge]"Line 18","Point 17"\[UndirectedEdge]"Line 18","Point 9"\[UndirectedEdge]"Line 19","Point 14"\[UndirectedEdge]"Line 19","Point 20"\[UndirectedEdge]"Line 19","Point 17"\[UndirectedEdge]"Line 19","Point 10"\[UndirectedEdge]"Line 20","Point 15"\[UndirectedEdge]"Line 20","Point 20"\[UndirectedEdge]"Line 20","Point 18"\[UndirectedEdge]"Line 20"}

leviGraph=Graph[edges,GraphLayout->"BipartiteEmbedding"]

Checks

The result gives the vertex count, edge count, degree counts, bipartiteness, connectedness, and automorphism-group order.

{VertexCount[leviGraph],EdgeCount[leviGraph],Counts[VertexDegree[leviGraph]],BipartiteGraphQ[leviGraph],ConnectedGraphQ[leviGraph],GroupOrder[GraphAutomorphismGroup[leviGraph]]}