ArticleOriginal scientific text
Title
k-Kernels and some operations in digraphs
Authors 1, 2
Affiliations
- Instituto de Matemáticas, Universidad Nacional Autónoma de México, Ciudad Universitaria, México, D.F. 04510, México
- Facultad de Ciencias, Universidad Nacional Autónoma de México, Ciudad Universitaria, Circuito Exterior, México, D.F. 04510, México
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.
Keywords
k-kernel, k-subdivision digraph, k-middle digraph and k-total digraph
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Pages:
39-49
Main language of publication
English
Received
2007-09-12
Accepted
2007-12-08
Published
2009
DOI: 10.7151/dmgt.1431
Exact and natural sciences