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.
@article{bwmeta1.element.doi-10_7151_dmgt_1912,
author = {Leila Asgharsharghi and Seyed Mahmoud Sheikholeslami and Lutz Volkmann},
title = {Signed Roman Edgek-Domination in Graphs},
journal = {Discussiones Mathematicae Graph Theory},
volume = {37},
year = {2017},
pages = {39-53},
zbl = {1354.05102},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.doi-10_7151_dmgt_1912}
}
Leila Asgharsharghi; Seyed Mahmoud Sheikholeslami; Lutz Volkmann. Signed Roman Edgek-Domination in Graphs. Discussiones Mathematicae Graph Theory, Tome 37 (2017) pp. 39-53. http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_7151_dmgt_1912/