On Kernels by Monochromatic Paths in \(D\)-join

Abstract

In \([2]\) it was introduced the concept of the kernel by monochromatic paths, which generalize concept of kernel. In this paper we prove the necessary and sufficient conditions for the existence of kernels by monochromatic paths in the \(D\)-join of digraphs. We also give sufficient condition for \(D\)-join to be monochromatic kernel perfect. The existence of generalized kernel (in distance sense) in D-join were studied in \([5]\). Moreover we calculate the total number of kernels by monochromatic paths in this product.