TY - JOUR

T1 - Enumeration of balanced finite group valued functions on directed graphs

AU - Cherniavsky, Yonah

AU - Goldstein, Avraham

AU - Levit, Vadim E.

AU - Shwartz, Robert

N1 - Publisher Copyright:
© 2016 Elsevier B.V. All rights reserved.

PY - 2016/7/1

Y1 - 2016/7/1

N2 - A group valued function on a graph is called balanced if the product of its values along any cycle is equal to the identity element of the group. We compute the number of balanced functions from the set of edges and vertices of a directed graph to a finite group considering two cases: when we are allowed to walk against the direction of an edge and when we are not allowed to walk against the edge direction. In the first case it appears that the number of balanced functions on edges and vertices depends on whether or not the graph is bipartite, while in the second case this number depends on the number of strong connected components of the graph.

AB - A group valued function on a graph is called balanced if the product of its values along any cycle is equal to the identity element of the group. We compute the number of balanced functions from the set of edges and vertices of a directed graph to a finite group considering two cases: when we are allowed to walk against the direction of an edge and when we are not allowed to walk against the edge direction. In the first case it appears that the number of balanced functions on edges and vertices depends on whether or not the graph is bipartite, while in the second case this number depends on the number of strong connected components of the graph.

KW - Balanced labelings of graphs

KW - Balanced signed graphs

KW - Combinatorial problems

KW - Consistent graphs

KW - Gain graphs

UR - http://www.scopus.com/inward/record.url?scp=84961785373&partnerID=8YFLogxK

U2 - 10.1016/j.ipl.2016.02.002

DO - 10.1016/j.ipl.2016.02.002

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AN - SCOPUS:84961785373

SN - 0020-0190

VL - 116

SP - 484

EP - 488

JO - Information Processing Letters

JF - Information Processing Letters

IS - 7

ER -