Compositions of Digraphs: A Survey

In this survey we overview known results and get several new results on digraph compositions which generalize several classes of digraphs, such as quasi-transitive digraphs. After an introductory section, the paper is divided into six sections: connectivity and linkages, kings and kernels, paths, cycles, acyclic spanning subdigraphs, strong spanning subdigraphs. This survey also contains some conjectures and open problems for further study.