MINIMAL RANKINGS OF THE CARTESIAN PRODUCT Kn Km

@inproceedings{Eyabi2012MINIMALRO,
  title={MINIMAL RANKINGS OF THE CARTESIAN PRODUCT Kn Km},
  author={Gilbert Eyabi and Jobby Jacob and Renu C. Laskar and Darren A. Narayan and Dan Pillone},
  year={2012}
}
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.