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Signed Roman Edgek-Domination in Graphs

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Asgharsharghi L., Sheikholeslami S. M., Volkmann L.

Discussiones Mathematicae Graph Theory

2017

tom 37

nr 1

39-53

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.

Ograniczanie wyników

1 Discussiones Mathematicae Graph Theory

1 Asgharsharghi L.

1 Sheikholeslami S. M.

1 Volkmann L.

1 2017

Wyniki wyszukiwania

Signed Roman Edgek-Domination in Graphs