# k-Kernels and some operations in digraphs

• Volume: 29, Issue: 1, page 39-49
• ISSN: 2083-5892

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## Abstract

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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 formed by these operations from another digraphs.

## How to cite

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Hortensia Galeana-Sanchez, and Laura Pastrana. "k-Kernels and some operations in digraphs." Discussiones Mathematicae Graph Theory 29.1 (2009): 39-49. <http://eudml.org/doc/270303>.

@article{HortensiaGaleana2009,
abstract = {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 formed by these operations from another digraphs.},
author = {Hortensia Galeana-Sanchez, Laura Pastrana},
journal = {Discussiones Mathematicae Graph Theory},
keywords = {k-kernel; k-subdivision digraph; k-middle digraph and k-total digraph; -kernel; -subdivision digraph; -middle digraph; -total digraph},
language = {eng},
number = {1},
pages = {39-49},
title = {k-Kernels and some operations in digraphs},
url = {http://eudml.org/doc/270303},
volume = {29},
year = {2009},
}

TY - JOUR
AU - Hortensia Galeana-Sanchez
AU - Laura Pastrana
TI - k-Kernels and some operations in digraphs
JO - Discussiones Mathematicae Graph Theory
PY - 2009
VL - 29
IS - 1
SP - 39
EP - 49
AB - 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 formed by these operations from another digraphs.
LA - eng
KW - k-kernel; k-subdivision digraph; k-middle digraph and k-total digraph; -kernel; -subdivision digraph; -middle digraph; -total digraph
UR - http://eudml.org/doc/270303
ER -

## References

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