Signed Roman Edgek-Domination in Graphs

Leila Asgharsharghi, Seyed Mahmoud Sheikholeslami, and Lutz Volkmann. "Signed Roman Edgek-Domination in Graphs." Discussiones Mathematicae Graph Theory 37.1 (2017): 39-53. <http://eudml.org/doc/288083>.

@article{LeilaAsgharsharghi2017,
abstract = {Let k ≥ 1 be an integer, and G = (V, E) be a finite and simple graph. The closed neighborhood NG[e] of an edge e in a graph G is the set consisting of e and all edges having a common end-vertex with e. A signed Roman edge k-dominating function (SREkDF) on a graph G is a function f : E → \{−1, 1, 2\} satisfying the conditions that (i) for every edge e of G, ∑x∈NG[e] f(x) ≥ k and (ii) every edge e for which f(e) = −1 is adjacent to at least one edge e′ for which f(e′) = 2. The minimum of the values ∑e∈E f(e), taken over all signed Roman edge k-dominating functions f of G is called the signed Roman edge k-domination number of G, and is denoted by γ′sRk(G). In this paper we initiate the study of the signed Roman edge k-domination in graphs and present some (sharp) bounds for this parameter.},
author = {Leila Asgharsharghi, Seyed Mahmoud Sheikholeslami, Lutz Volkmann},
journal = {Discussiones Mathematicae Graph Theory},
keywords = {signed Roman edge k-dominating function; signed Roman edge k-domination number; signed Roman edge -dominating function; signed Roman edge -domination number},
language = {eng},
number = {1},
pages = {39-53},
title = {Signed Roman Edgek-Domination in Graphs},
url = {http://eudml.org/doc/288083},
volume = {37},
year = {2017},
}

TY - JOUR
AU - Leila Asgharsharghi
AU - Seyed Mahmoud Sheikholeslami
AU - Lutz Volkmann
TI - Signed Roman Edgek-Domination in Graphs
JO - Discussiones Mathematicae Graph Theory
PY - 2017
VL - 37
IS - 1
SP - 39
EP - 53
AB - Let k ≥ 1 be an integer, and G = (V, E) be a finite and simple graph. The closed neighborhood NG[e] of an edge e in a graph G is the set consisting of e and all edges having a common end-vertex with e. A signed Roman edge k-dominating function (SREkDF) on a graph G is a function f : E → {−1, 1, 2} satisfying the conditions that (i) for every edge e of G, ∑x∈NG[e] f(x) ≥ k and (ii) every edge e for which f(e) = −1 is adjacent to at least one edge e′ for which f(e′) = 2. The minimum of the values ∑e∈E f(e), taken over all signed Roman edge k-dominating functions f of G is called the signed Roman edge k-domination number of G, and is denoted by γ′sRk(G). In this paper we initiate the study of the signed Roman edge k-domination in graphs and present some (sharp) bounds for this parameter.
LA - eng
KW - signed Roman edge k-dominating function; signed Roman edge k-domination number; signed Roman edge -dominating function; signed Roman edge -domination number
UR - http://eudml.org/doc/288083
ER -