Signed Roman Edge k-Domination in Graphs

• Main Authors: Asgharsharghi Leila, Sheikholeslami Seyed Mahmoud, Volkmann Lutz
• Format: Article
• Language: English
• Published: Sciendo 2017-02-01
• Series: Discussiones Mathematicae Graph Theory
• Subjects: signed roman edge k-dominating function; signed roman edge k-domination number; 05c69
• Online Access: https://doi.org/10.7151/dmgt.1912

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∈Ef(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.