Signed Total Roman Domination in Digraphs

Lutz Volkmann

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The signed k-domination number of directed graphs

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Some remarks about digraphs with nonisomorphic $1$ - or $2$ -neighbourhoods

Halina Bielak, Elżbieta Soczewińska (1983)

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New proofs of the uniqueness of extremal noneven digraphs.

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Randomly Eulerian digraphs

Gary Chartrand, Don R. Lick (1971)

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On (4, 2)-digraphs containing a cycle of length 2.

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The k-Rainbow Bondage Number of a Digraph

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

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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...

On minimal regular digraphs with given girth

Mehdi Behzad, Gary Chartrand, Curtiss Wall (1970)

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k-Kernels and some operations in digraphs

Hortensia Galeana-Sanchez, Laura Pastrana (2009)

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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...