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The domination number γ of a graph G is the minimum cardinality of a subset D of vertices of G such that each vertex outside D is adjacent to at least one vertex in D. For any subset A of the vertex set of G, let + (A) be the set of vertices not in A which are adjacent to at least one vertex in A. Let N(A) be the union of A and + (A), and d(A) be the sum of degrees of all the vertices...
For an integer-valued function f defined on the vertices of a graph G, the f-domination number γ f (G) of G is the smallest cardinality of a subset D V(G) such that each x V(G) - D is adjacent to at least f(x) vertices in D. When f(x) = k for all x V(G), γ f (G) is the k-domination number γ k (G). In this note, we give a tight upper bound for γ f and an improvement...
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