Enumerating topological (nk)(nk)-configurations

An (nk)(nk)-configuration is a set of n points and n lines in the projective plane such that their point–line incidence graph is k-regular. The configuration is geometric, topological, or combinatorial depending on whether lines are considered to be straight lines, pseudolines, or just combinatorial lines.We provide an algorithm for generating, for given n and k  , all topological (nk)(nk)-configurations up to combinatorial isomorphism, without enumerating first all combinatorial (nk)(nk)-configurations. We apply this algorithm to confirm efficiently a former result on topological (184)(184)-configurations, from which we obtain a new geometric (184)(184)-configuration. Preliminary results on (194)(194)-configurations are also briefly reported.