Displaying similar documents to “Edge domination in graphs of cubes”

Signed Roman Edgek-Domination in Graphs

Leila Asgharsharghi, Seyed Mahmoud Sheikholeslami, Lutz Volkmann (2017)

Discussiones Mathematicae Graph Theory

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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...