Counting Unlabelled Topologies and Transitive Relations

Abstract

A classification of various types of unlabled topologies and transition relations that counts up to 15 or 16 points was discussed. Only directed graphs (digraphs) that do not have multiple edges but may have up to one loop point were considered for the computation. A strong component of a digraph was a maximal set of points such that there was a directed path within P from x to y for each pair x, y ⊂ P. It was found that two digraphs were isomorphic if there was a bijection between their point-set that induces a bijection between their edge-sets. Show more