On \((k,l)\) – Kernels of Orientations of Special Graphs

In [1], [2] we can find results concerning kernel-perfect graphs and solvable graphs. These concepts are related to kernels of a digraph. The authors of [2] consider two graph constructions: the join of two graphs and duplication of a vertex. These kinds of graphs preserve kernel-perfectness and solvability of their orientations. In this paper we generalize results from [2] applying them to \((k,l)\)-kernels and two operations: generalized join and duplication of a subset of vertices. The concept of a \((k,l)\)-kernel of a digraph was introduced in [8] and was studied in [6], [7], and [9]. In our considerations we take advantage of the asymmetrical part of digraphs, which was used by H. Galeana-Sanchez in [6] in the proof of a sufficient condition for a digraph to have a \((k, l)\)-kernel.