K- Kernels in Digraphs Formed by some Operations from other Digraphs

Abstract

Let k ≥ 2 be a positive integer. For a digraph D, a set J ⊆ V (D) is said to be a k- kernel of D if for every x, y ∈ J; d_D(x, y) ≥ k and for every z ∈ V (D) ∖ J, there exists w ∈ J such that d_D(z,w) ≤ k - 1: Given a digraph D; as a generalisation of the operations defined in [9], we define operations on D; each of which results in a digraph with a k- kernel.

Key words and phrases. k- independence, ℓ- absorbence, (k, ℓ)- kernel.

2010 Mathematics Subject Classification. 05C20, 05C69