# k-Kernels and some operations in digraphs

Hortensia Galeana-Sanchez; Laura Pastrana

Discussiones Mathematicae Graph Theory (2009)

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

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topHortensia 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 -

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