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2006

Minimal rankings and the arank number of a path

13 years 11 months ago
Minimal rankings and the arank number of a path
Given a graph G, a function f : V (G) {1, 2, . . . , k} is a k-ranking of G if f (u) = f (v) implies every u - v path contains a vertex w such that f (w) > f (u). A k-ranking is minimal if the reduction of any label greater than 1 violates the described ranking property. The arank number of a graph, denoted r(G), is the largest k such that G has a minimal k-ranking. We present new results involving minimal k-rankings of paths. In particular, we determine r(Pn), a problem posed by Laskar and Pillone in 2000.
Victor Kostyuk, Darren A. Narayan, Victoria A. Wil
Added 11 Dec 2010
Updated 11 Dec 2010
Type Journal
Year 2006
Where DM
Authors Victor Kostyuk, Darren A. Narayan, Victoria A. Williams
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