Displaying similar documents to “Signed Total Roman Domination in Digraphs”

The k-Rainbow Bondage Number of a Digraph

Jafar Amjadi, Negar Mohammadi, Seyed Mahmoud Sheikholeslami, Lutz Volkmann (2015)

Discussiones Mathematicae Graph Theory

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Let D = (V,A) be a finite and simple digraph. A k-rainbow dominating function (kRDF) of a digraph D is a function f from the vertex set V to the set of all subsets of the set {1, 2, . . . , k} such that for any vertex v ∈ V with f(v) = Ø the condition ∪u∈N−(v) f(u) = {1, 2, . . . , k} is fulfilled, where N−(v) is the set of in-neighbors of v. The weight of a kRDF f is the value w(f) = ∑v∈V |f(v)|. The k-rainbow domination number of a digraph D, denoted by γrk(D), is the minimum weight...

k-Kernels and some operations in digraphs

Hortensia Galeana-Sanchez, Laura Pastrana (2009)

Discussiones Mathematicae Graph Theory

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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...

Degree sequences of digraphs with highly irregular property

Zofia Majcher, Jerzy Michael (1998)

Discussiones Mathematicae Graph Theory

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A digraph such that for each its vertex, vertices of the out-neighbourhood have different in-degrees and vertices of the in-neighbourhood have different out-degrees, will be called an HI-digraph. In this paper, we give a characterization of sequences of pairs of out- and in-degrees of HI-digraphs.

Twin Minus Total Domination Numbers In Directed Graphs

Nasrin Dehgardi, Maryam Atapour (2017)

Discussiones Mathematicae Graph Theory

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Let D = (V,A) be a finite simple directed graph (shortly, digraph). A function f : V → {−1, 0, 1} is called a twin minus total dominating function (TMTDF) if f(N−(v)) ≥ 1 and f(N+(v)) ≥ 1 for each vertex v ∈ V. The twin minus total domination number of D is y*mt(D) = min{w(f) | f is a TMTDF of D}. In this paper, we initiate the study of twin minus total domination numbers in digraphs and we present some lower bounds for y*mt(D) in terms of the order, size and maximum and minimum in-degrees...