Bokowski-Schewe Graph

Author

Eric W. Weisstein
July 31, 2026

This notebook downloaded from https://mathworld.wolfram.com/notebooks/GraphTheory/Bokowski-ScheweGraph.nb.

For more information, see Eric's MathWorld entry https://mathworld.wolfram.com/Bokowski-ScheweGraph.html.

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

Sources

Levi graph of the Bokowski-Schewe configuration. Source: J. Bokowski and V. Pilaud, Enumerating Topological (n_k)-Configurations, Computational Geometry 47 (2014), 175-186, https://doi.org/10.1016/j.comgeo.2012.10.002; https://arxiv.org/abs/1210.0306.

Incidence data

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

Levi graph

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

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]]}