Generating connected and 2-edge connected graphs

Abstract

We focus on the algorithm underlying the main result of []. This is an algebraic formula to generate all connected graphs in a recursive and efficient manner. The key feature is that each graph carries a scalar factor given by the inverse of the order of its group of automorphisms. In the present paper, we revise that algorithm on the level of graphs. Moreover, we extend the result subsequently to further classes of connected graphs, namely, \two-edge connected, simple and loopless graphs. Our method consists of basic graph transformations only.