Generalized exponents of boolean matrices

In 1990 Brualdi and Liu (J. Graph Theory 14 (1990) 483) introduced the concept of generalized exponent for primitive Boolean matrices. In the study of generalized exponents, we focus on problems of the following three types: (1) To determine the maxima (namely, the exact upper bounds) of all kinds of generalized exponents; (2) To characterize the extreme matrices completely; (3) To determine the sets of exponents (including the existence of gaps and their distributions). In this survey we will describe respectively the developments of these problems in recent years.