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

Y Cherniaysky

Department of Mathematics

Ariel University

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

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

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Cite this

@article{2018c61416b242dfab32701bb93d1b5e,

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

author = "Y Cherniaysky",

note = "Times Cited in Web of Science Core Collection: 0 Total Times Cited: 0 Cited Reference Count: 23",

year = "2019",

language = "الإنجليزيّة",

volume = "22",

pages = "75--101",

journal = "Advances and Applications in Discrete Mathematics",

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AU - Cherniaysky, Y

N1 - Times Cited in Web of Science Core Collection: 0 Total Times Cited: 0 Cited Reference Count: 23

PY - 2019

Y1 - 2019

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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. 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.

KW - FLOWS

KW - GROUP-VALUED FUNCTIONS

KW - LATTICE

KW - TENSION POLYNOMIALS

KW - balanced labelings of graphs

KW - balanced signed graphs

KW - consistent graphs

KW - cycle-vanishing valuations

KW - gain graphs

KW - weighted graphs

M3 - مقالة

SN - 0974-1658

VL - 22

SP - 75

EP - 101

JO - Advances and Applications in Discrete Mathematics

JF - Advances and Applications in Discrete Mathematics

IS - 1

ER -