# Signed Total Roman Edge Domination In Graphs

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

top

## Abstract

top
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.

## How to cite

top

Leila 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 -

## NotesEmbed?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.