semikernels

— Moreover, if llt;k and the girth of D is at least l#43;1, then these two numbers are equal. The number of semikernels of D is equal to the number of semikernels of #92;mathcal#123;L#125;D. Also we introduce the concept of (k,l)-Grundy function as a generalization of the concept of Grundy function and we prove that the number of (k,l)-Grundy functions of D is equal to the number of (k,l)-Grundy functions of any partial line digraph #92;mathcal#123;L#125;D..