Let k ∈ Z +. A − distance Roman dominating function (kDRDF) on G = (V, E) is a f : V → {0, 1, 2} such that for every vertex v with f(v) 0, there u f(u) 2 d(u, v) ≤ k. The global (GkDRDF) if and only its complement G. weight of the value w(f) P x∈V f(x). minimum graph called domination number denoted as γ gR(G). gR(G) Note that, 1 usual γgR(G), is, γgR(G). authors initiated this study. In paper,...

The concepts of covering and matching in fuzzy graphs using strong arcs are introduced and obtained the relationship between them analogous to Gallai’s results in graphs. The notion of paired domination in fuzzy graphs using strong arcs is also studied. The strong paired domination number γspr of complete fuzzy graph and complete bipartite fuzzy graph is determined and obtained bounds for the s...