Configurations graphs of neighbourhood geometries

Congurations of type ( 2 + 1) give rise to {regular sim- ple graphs via congur ation graphs. On the other hand, neighbourhood geometries of C4{free {regular simple graphs on 2 + 1 vertices turn out to be congurations of type ( 2 + 1) . We investigate which cong- urations of type ( 2 + 1) are equal or isomorphic to the neighbourhood geometry of their conguration graph and conversely. We classify all such graphs and congurations for = 3 and for = 4 when the graphs admit a centre of radius 2.