# Additive Edge Labelings - Mathematics > Combinatorics

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Abstract: Let G=V,E be a graph and d a positive integer. We study the followingproblem: for which labelings f E: E \to Z d is there a labeling f V:V \to Z dsuch that f Ei,j = f Vi + f Vj mod d, for every edge i,j in E? Wealso explore the connections of the equivalent multiplicative version to toricideals. We derive a polynomial algorithm to answer these questions and toobtain all possible solutions.

Author: Alicia Dickenstein, Enrique A. Tobis

Source: https://arxiv.org/