Discussiones Mathematicae Graph Theory 29(1) (2009)
39-49
DOI: https://doi.org/10.7151/dmgt.1431
k-KERNELS AND SOME OPERATIONS IN DIGRAPHS
Hortensia Galeana-Sanchez
Instituto de Matemáticas | Laura Pastrana
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.
2000 Mathematics Subject Classification: Primary: 05C20; Secondary: 05C69.
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Received 12 September 2007
Revised 8 December 2007
Accepted 29 December 2008
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