MINIMAL RANKINGS OF THE CARTESIAN PRODUCT Kn Km
نویسندگان
چکیده
For a graph G = (V,E), a function f : V (G) → {1, 2, . . . , k} is a kranking 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, ψr(G), of G is the maximum value of k such that G has a minimal k-ranking. We completely determine the arank number of the Cartesian product Kn Kn, and we investigate the arank number of Kn Km where n > m.
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