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For a graph G = (V, E), a function f : V (G) → {1, 2,. .. , k} is a k-ranking if f (u) = f (v) implies that every u−v path contains a vertex w such that f (w) > f (u). A k-ranking is minimal if decreasing any label violates the definition of ranking. The arank number, ψ r (G), of G is the maximum value of k such that G has a minimal k-ranking. We completely… (More)

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