Groups of balanced labelings on graphs

Yonah Cherniavsky, Avraham Goldstein, Vadim E. Levit

Research output: Contribution to journalArticlepeer-review

3 Scopus citations


We discuss functions from edges and vertices of an undirected graph to an Abelian group. Such functions, when the sum of their values along any cycle is zero, are called balanced labelings. The set of balanced labelings forms an Abelian group. We study the structure of this group and the structure of two other groups, closely related to it: the subgroup of balanced labelings which consists of functions vanishing on vertices and the corresponding factor-group. This work is completely self-contained, except the algorithm for obtaining the 3-edge-connected components of an undirected graph, for which we make appropriate references to the literature.

Original languageEnglish
Pages (from-to)15-25
Number of pages11
JournalDiscrete Mathematics
Issue number1
StatePublished - 6 Apr 2014


  • Balanced signed graphs
  • Consistent marked graphs
  • Gain graphs
  • Voltage graphs
  • k-edge connectivity


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