k-Kernels and some operations in digraphs

Hortensia Galeana-Sánchez, Laura Pastrana
2009 Discussiones Mathematicae Graph Theory  
Let D be a digraph. V (D) denotes the set of vertices of D; a set N ⊆ V (D) is said to be a k-kernel of D if it satisfies the following two conditions: for every pair of different vertices u, v ∈ N it holds that every directed path between them has length at least k and for every vertex x ∈ V (D) − N there is a vertex y ∈ N such that there is an xy-directed path of length at most k − 1. In this paper, we consider some operations on digraphs and prove the existence of k-kernels in digraphs
more » ... s in digraphs formed by these operations from another digraphs.
doi:10.7151/dmgt.1431 fatcat:qji2zscphzetflh2ufmaweoz3y