Enumeration of balanced finite group valued functions on directed graphs

Yonah Cherniavsky; Avraham Goldstein; Vadim E. Levit; Robert Shwartz

doi:10.1016/j.ipl.2016.02.002

Enumeration of balanced finite group valued functions on directed graphs

Yonah Cherniavsky, Avraham Goldstein, Vadim E. Levit, Robert Shwartz

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

1 Scopus citations

Abstract

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.

Original language	English
Pages (from-to)	484-488
Number of pages	5
Journal	Information Processing Letters
Volume	116
Issue number	7
DOIs	https://doi.org/10.1016/j.ipl.2016.02.002
State	Published - 1 Jul 2016

Keywords

Balanced labelings of graphs
Balanced signed graphs
Combinatorial problems
Consistent graphs
Gain graphs

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10.1016/j.ipl.2016.02.002

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Enumeration of balanced finite group valued functions on directed graphs

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Keywords

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