Signed Total Roman Domination in Digraphs

• Autorzy: Lutz Volkmann
• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

digraph; signed total Roman dominating function; signed total Roman domination number

Kategorie tematyczne

• 05C20: Directed graphs (digraphs), tournaments
• 05C69: Dominating sets, independent sets, cliques

• Wydawca: De Gruyter Open
• Czasopismo: Discussiones Mathematicae Graph Theory
• Rocznik: 2017
• Tom: 37
• Numer: 1
• Strony: 261-272

Daty

wydano

2017-02-01

otrzymano

2015-08-28

poprawiono

2016-04-15

zaakceptowano

2016-04-15

online

2017-01-13

Twórcy

autor

Lutz Volkmann

• Lehrstuhl II für Mathematik, RWTH Aachen University, 52056 Aachen,

Identyfikatory

DOI

10.7151/dmgt.1929