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Rank numbers for bent ladders

Peter RichterEmily LevenAnh TranBryan EkJobby JacobDarren A. Narayan — 2014

Discussiones Mathematicae Graph Theory

A ranking on a graph is an assignment of positive integers to its vertices such that any path between two vertices with the same label contains a vertex with a larger label. The rank number of a graph is the fewest number of labels that can be used in a ranking. The rank number of a graph is known for many families, including the ladder graph P2 × Pn. We consider how ”bending” a ladder affects the rank number. We prove that in certain cases the rank number does not change, and in others the rank...

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