Wyniki wyszukiwania

Wyszukiwano:
w słowach kluczowych: signed total Roman dominating function

Sortuj według:

Ogranicz wyniki do:

Signed Total Roman Domination in Digraphs

100%

Volkmann L.

Discussiones Mathematicae Graph Theory

2017

tom 37

nr 1

261-272

Let D be a finite and simple digraph with vertex set V (D). A signed total Roman dominating function (STRDF) on a digraph D is a function f : V (D) → {−1, 1, 2} satisfying the conditions that (i) ∑x∈N−(v) f(x) ≥ 1 for each v ∈ V (D), where N−(v) consists of all vertices of D from which arcs go into v, and (ii) every vertex u for which f(u) = −1 has an inner neighbor v for which f(v) = 2. The weight of an STRDF f is w(f) = ∑v∈V (D) f(v). The signed total Roman domination number γstR(D) of D is the minimum weight of an STRDF on D. In this paper we initiate the study of the signed total Roman domination number of digraphs, and we present different bounds on γstR(D). In addition, we determine the signed total Roman domination number of some classes of digraphs. Some of our results are extensions of known properties of the signed total Roman domination number γstR(G) of graphs G.

Signed Total Roman Edge Domination In Graphs

100%

Asgharsharghi L., Sheikholeslami S. M.

Discussiones Mathematicae Graph Theory

2017

tom 37

nr 4

1039-1053

Let G = (V,E) be a simple graph with vertex set V and edge set E. A signed total Roman edge dominating function of G is a function f : Ʃ → {−1, 1, 2} satisfying the conditions that (i) Ʃe′∈N(e) f(e′) ≥ 1 for each e ∈ E, where N(e) is the open neighborhood of e, and (ii) every edge e for which f(e) = −1 is adjacent to at least one edge e′ for which f(e′) = 2. The weight of a signed total Roman edge dominating function f is !(f) = Ʃe∈E f(e). The signed total Roman edge domination number y′stR(G) of G is the minimum weight of a signed total Roman edge dominating function of G. In this paper, we first prove that for every tree T of order n ≥ 4, y′stR(T) ≥ 17−2n/5 and we characterize all extreme trees, and then we present some sharp bounds for the signed total Roman edge domination number. We also determine this parameter for some classes of graphs.

Ograniczanie wyników

2 Discussiones Mathematicae Graph Theory

1 Asgharsharghi L.

1 Sheikholeslami S. M.

1 Volkmann L.

2 2017

Wyniki wyszukiwania

Signed Total Roman Domination in Digraphs

Signed Total Roman Edge Domination In Graphs