ALGEBRAIC STRUCTURES RELATED TO BALANCED FUNCTIONS ON GRAPHS: RESULTS AND OPEN PROBLEMS

Y Cherniaysky

ALGEBRAIC STRUCTURES RELATED TO BALANCED FUNCTIONS ON GRAPHS: RESULTS AND OPEN PROBLEMS

Department of Mathematics

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

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. Such functions themselves form a group. In this expository article we discuss our rather recent works on this subject and suggest problems for further investigation.

Original language	English
Pages (from-to)	75-101
Number of pages	27
Journal	Advances and Applications in Discrete Mathematics
Volume	22
Issue number	1
State	Published - 2019

Keywords

consistent graphs
balanced signed graphs
balanced labelings of graphs
gain graphs
weighted graphs
cycle-vanishing valuations
GROUP-VALUED FUNCTIONS
TENSION POLYNOMIALS
LATTICE
FLOWS

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Cite this

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title = "ALGEBRAIC STRUCTURES RELATED TO BALANCED FUNCTIONS ON GRAPHS: RESULTS AND OPEN PROBLEMS",

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. Such functions themselves form a group. In this expository article we discuss our rather recent works on this subject and suggest problems for further investigation.",

keywords = "consistent graphs, balanced signed graphs, balanced labelings of graphs, gain graphs, weighted graphs, cycle-vanishing valuations, GROUP-VALUED FUNCTIONS, TENSION POLYNOMIALS, LATTICE, FLOWS",

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KW - TENSION POLYNOMIALS

KW - LATTICE

KW - FLOWS

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ALGEBRAIC STRUCTURES RELATED TO BALANCED FUNCTIONS ON GRAPHS: RESULTS AND OPEN PROBLEMS

Abstract

Keywords

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