Abstract:
It is proved that the number of semikernels (quasi kernels) of a digraph D is less than or equal to the number of semikernels (quasi kernels) of its line digraph L(D). It is also proved that the number of Grundy functions of D is equal to the number of Grundy functions of its line digraph L(D) (in the case where every vertex of D has indegree at least one).