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Given a graph G, a function f : V (G)→ {1, 2, ..., k} is a k-biranking of G if f(u) = f(v) implies every u-v path contains vertices x and y such that f(x) > f(u) and f(y) < f(u). The birank number of a graph, denoted bi(G), is the minimum k such that G has a k-biranking. In this paper we determine the birank numbers for ladder, prism, and Möbius ladder graphs.
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ژورنال
عنوان ژورنال: Physical Review B
سال: 1998
ISSN: 0163-1829,1095-3795
DOI: 10.1103/physrevb.58.443