Structure of the Group of Balanced Labelings on Graphs, its Subgroups and Quotient Groups

2013/01/17 by Yonah Cherniavsky, Cherniavsky, Yonah, Avraham Goldstein +3
Computer Science · Mathematics · #Advanced Graph Theory Research #Combinatorics (math.CO) #FOS: Mathematics #Graph Labeling and Dimension Problems #Graph Theory and Algorithms #Group Theory (math.GR) #math.CO #math.GR

paper · pdf · doi:10.48550/arxiv.1301.4206

22 pages

openalex publication_date 2013/01/17 · arxiv created 2013/06/27 · arxiv updated 2013/06/28 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28

Abstract

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 closely related to it groups: 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.

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