# Signed Total Roman Edge Domination In Graphs

Leila Asgharsharghi; Seyed Mahmoud Sheikholeslami

Discussiones Mathematicae Graph Theory (2017)

- Volume: 37, Issue: 4, page 1039-1053
- ISSN: 2083-5892

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topLeila Asgharsharghi, and Seyed Mahmoud Sheikholeslami. "Signed Total Roman Edge Domination In Graphs." Discussiones Mathematicae Graph Theory 37.4 (2017): 1039-1053. <http://eudml.org/doc/288435>.

@article{LeilaAsgharsharghi2017,

abstract = {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.},

author = {Leila Asgharsharghi, Seyed Mahmoud Sheikholeslami},

journal = {Discussiones Mathematicae Graph Theory},

keywords = {signed total Roman dominating function; signed total Roman domination number; signed total Roman edge dominating function; signed total Roman edge domination number.},

language = {eng},

number = {4},

pages = {1039-1053},

title = {Signed Total Roman Edge Domination In Graphs},

url = {http://eudml.org/doc/288435},

volume = {37},

year = {2017},

}

TY - JOUR

AU - Leila Asgharsharghi

AU - Seyed Mahmoud Sheikholeslami

TI - Signed Total Roman Edge Domination In Graphs

JO - Discussiones Mathematicae Graph Theory

PY - 2017

VL - 37

IS - 4

SP - 1039

EP - 1053

AB - 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.

LA - eng

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

UR - http://eudml.org/doc/288435

ER -

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