Cograph generation with linear delay

Cographs have always been a research target in areas such as coloring, graph decomposition, and spectral theory. In this work, we present an algorithm to generate all unlabeled cographs with \(n\) vertices, based on the generation of cotrees. The delay of our algorithm (time spent between two consecutive outputs) is \(O(n)\). The time needed to generate the first output is also \(O(n)\), which gives an overall \(O(n\,M_n)\) time complexity, where \(M_n\) is the number of unlabeled cographs with \(n\) vertices. The algorithm avoids the generation of duplicates (isomorphic outputs) and produces, as a by-product, a linear ordering of unlabeled cographs wih \(n\) vertices.