Twin signed k-domination numbers in directed graphs
Keyword(s):
Let D = (V;A) be a finite simple directed graph (digraph). A function f : V ? {-1,1} is called a twin signed k-dominating function (TSkDF) if f (N-[v]) ? k and f (N+[v]) ? k for each vertex v ? V. The twin signed k-domination number of D is ?* sk(D) = min{?(f)?f is a TSkDF of D}. In this paper, we initiate the study of twin signed k-domination in digraphs and present some bounds on ?* sk(D) in terms of the order, size and maximum and minimum indegrees and outdegrees, generalising some of the existing bounds for the twin signed domination numbers in digraphs and the signed k-domination numbers in graphs. In addition, we determine the twin signed k-domination numbers of some classes of digraphs.
2016 ◽
Vol 47
(3)
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pp. 357-371
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2018 ◽
Vol 11
(03)
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pp. 1850034
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2005 ◽
Vol 55
(2)
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pp. 479-482
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2009 ◽
Vol 309
(8)
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pp. 2567-2570
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2011 ◽
Vol 65
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pp. 145-147
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2016 ◽
Vol 10
(1)
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pp. 65-72
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2019 ◽
Vol 12
(07)
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pp. 2050004
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