Quasi-Kernels for Oriented Paths and Cycles

Abstract

If D is a digraph, then K∈V(D) is a quasi-kernel of D if D［K］is discrete and for each y∈V(D)－K there is x∈K such that the directed distance from y to x is less than three. We give formulae for the number of quasi-kernels and for the number of minimal quasi-kernels of oriented paths and cycles.