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 -