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2009 | 29 | 1 | 39-49
Tytuł artykułu

k-Kernels and some operations in digraphs

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
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.
Wydawca
Rocznik
Tom
29
Numer
1
Strony
39-49
Opis fizyczny
Daty
wydano
2009
otrzymano
2007-09-12
poprawiono
2007-12-08
zaakceptowano
2008-12-29
Twórcy
  • 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
Bibliografia
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  • [4] P. Duchet and H. Meyniel, A note on kernel-critical graphs, Discrete Math. 33 (1981) 103-105, doi: 10.1016/0012-365X(81)90264-8.
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  • [13] M. Kucharska and M. Kwaśnik, On (k,l)-kernels of superdigraphs of Pₘ and Cₘ, Discuss. Math. Graph Theory 21 (2001) 95-109, doi: 10.7151/dmgt.1135.
  • [14] M. Kwaśnik, The generalization of Richardson theorem, Discuss. Math. IV (1981) 11-13.
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  • [16] M. Blidia, P. Duchet, H. Jacob, F. Maffray and H. Meyniel, Some operations preserving the existence of kernels, Discrete Math. 205 (1999) 211-216, doi: 10.1016/S0012-365X(99)00026-6.
  • [17] M. Richardson, Extensions theorems for solutions of irreflexive relations, Proc. Mat. Acad. Sci. 39 (1953) 649-655, doi: 10.1073/pnas.39.7.649.
  • [18] M. Richardson, Solutions of irreflexive relations, Ann. Math. 58 (1953) 573-590, doi: 10.2307/1969755.
  • [19] J. Topp, Kernels of digraphs formed by some unary operations from other digraphs, J. Rostock Math. Kolloq. 21 (1982) 73-81.
  • [20] J. von Neumann and O. Morgenstern, Theory of games and economic behavior (Princeton University Press, Princeton, 1944).
  • [21] A. Włoch and I. Włoch, On (k,l)-kernels in generalized products, Discrete Math. 164 (1997) 295-301, doi: 10.1016/S0012-365X(96)00064-7.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.bwnjournal-article-doi-10_7151_dmgt_1431
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