The terms "Berman 
graph" and "Berman 
graph" are used in this work for the Levi
graphs of the corresponding Berman configurations.
They are connected, bipartite, Hamiltonian,
and nonplanar. Both have girth
6 and radius 5. Since both configurations are self-dual,
each graph has an automorphism that interchanges
the two parts of its bipartition.
| graph | vertices | edges | degree | diameter |  |
Berman  graph | 96 | 240 | 5 | 5 | 48 |
Berman  graph | 192 | 576 | 6 | 5 | 192 |
The graphs are implemented in the Wolfram Language as GraphData["Berman485Graph"] and GraphData["Berman966Graph"].
