TY - JOUR

T1 - Groups of balanced labelings on graphs

AU - Cherniavsky, Yonah

AU - Goldstein, Avraham

AU - Levit, Vadim E.

PY - 2014/4/6

Y1 - 2014/4/6

N2 - 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.

AB - 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.

KW - Balanced signed graphs

KW - Consistent marked graphs

KW - Gain graphs

KW - Voltage graphs

KW - k-edge connectivity

UR - http://www.scopus.com/inward/record.url?scp=84896521422&partnerID=8YFLogxK

U2 - 10.1016/j.disc.2013.12.003

DO - 10.1016/j.disc.2013.12.003

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AN - SCOPUS:84896521422

SN - 0012-365X

VL - 320

SP - 15

EP - 25

JO - Discrete Mathematics

JF - Discrete Mathematics

IS - 1

ER -