The term "Fabrici-Madaras graphs" is used in this work for two 1-planar graphs constructed by Fabrici and Madaras (2007): a 24-vertex 7-regular graph showing that the upper bound of 7 on the minimum vertex degree of a 1-planar graph is sharp, and a 56-vertex cubic graph showing that a 1-planar graph of minimum vertex degree 3 can attain girth 7. The 24-vertex member is the crossed elongated square gyrobicupola graph, meaning that every pair of vertices lying on a common face of the polyhedron is joined by an edge.
Both graphs are Hamiltonian graphs with 84 edges. Their additional properties are summarized below.
| graph | vertex degree | girth | graph crossing number | rectilinear crossing number |
| 24-Fabrici-Madaras graph | 7 | 3 | 18 | 18 |
| 56-Fabrici-Madaras graph | 3 | 7 | 14 | 14 |
The 56-Fabrici-Madaras graph is also a unit-distance graph.
The graphs are implemented in the Wolfram Language as GraphData["FabriciMadarasGraph24"] and GraphData["FabriciMadarasGraph56"], respectively.
