Signed Total Roman Edge Domination In Graphs

• Autorzy: Leila Asgharsharghi , Seyed Mahmoud Sheikholeslami
• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

signed total Roman dominating function; signed total Roman domination number; signed total Roman edge dominating function; signed total Roman edge domination number.

• Wydawca: De Gruyter Open
• Czasopismo: Discussiones Mathematicae Graph Theory
• Rocznik: 2017
• Tom: 37
• Numer: 4
• Strony: 1039-1053

Daty

wydano

2017-11-27

otrzymano

2016-04-25

poprawiono

2016-08-27

zaakceptowano

2016-08-27

online

2017-09-02

Twórcy

autor

Leila Asgharsharghi

• , I.R.

autor

Seyed Mahmoud Sheikholeslami

• , I.R.

Identyfikatory

DOI

10.7151/dmgt.1984