Additive Edge Labelings

Details Additive Edge Labelings Additive Edge Labelings

2009-04-16

arxiv.org/abs/0904.2600v1

Mathematics

Combinatorics

14 pages

Scientific paper

Let G=(V,E) be a graph and d a positive integer. We study the following problem: for which labelings f_E: E \to Z_d is there a labeling f_V:V \to Z_d such that f_E(i,j) = f_V(i) + f_V(j) (mod d), for every edge (i,j) in E? We also explore the connections of the equivalent multiplicative version to toric ideals. We derive a polynomial algorithm to answer these questions and to obtain all possible solutions.

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