Classification of three families 5-configurations

The structure of three currently known infinite series of 5-configurations on countable sets X is investigated. Configurations of series A and B are constructed from so-called oriented 2-graphs, in which each vertex has two incoming and two outgoing arcs, and there are no loops or parallel arcs. Each vertex of the 2-graph corresponds to two points of the set X for configurations of series A and four points for configurations of series B. Configurations of series C are constructed from an oriented 1-graph: each vertex has one incoming and one outgoing arc, and each vertex corresponds to three points of the set X. It is proved that configurations of different series are not isomorphic to each other, and that two configurations of series A, like two configurations in general position of series B, are isomorphic if and only if the corresponding 2-graphs are isomorphic.