Abstract

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 ψr(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 ψr(Pn), a problem posed by Laskar and Pillone in 2000 (Refer to PDF file for exact formulas).

Publication Date

8-28-2006

Comments

Copyright 2006 Elsevier Science B.V., Amsterdam. All Rights Reserved. Research travel support provided by JetBlue Airways, Kay & Tony Carlisi, and Timothy Gilbert. Partially partially supported by a RIT COS Dean’s Summer Research Fellowship Grant.ISSN:0012-365X Note: imported from RIT’s Digital Media Library running on DSpace to RIT Scholar Works in February 2014.

Document Type

Article

Department, Program, or Center

School of Mathematical Sciences (COS)

Campus

RIT – Main Campus

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