English

Additive Edge Labelings

Combinatorics 2009-04-20 v1

Abstract

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.

Cite

@article{arxiv.0904.2600,
  title  = {Additive Edge Labelings},
  author = {Alicia Dickenstein and Enrique A. Tobis},
  journal= {arXiv preprint arXiv:0904.2600},
  year   = {2009}
}

Comments

14 pages

R2 v1 2026-06-21T12:52:19.083Z