Harmonic labeling of graphs

Itai Benjamini; Van Cyr; Eviatar B. Procaccia; Ran J. Tessler

doi:10.1016/j.disc.2013.04.022

Harmonic labeling of graphs

Itai Benjamini, Van Cyr, Eviatar B. Procaccia, Ran J. Tessler

Department of Mathematics

Weizmann Institute of Science

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

Abstract

Which graphs admit an integer valued harmonic function which is injective and surjective onto Z^d Such a function, which we call harmonic labeling, is constructed when the graph is the lattice ^Zd. It is shown that for any finite graph G containing at least one edge, there is no harmonic labeling of G×Z. Further discussion and open problems are presented.

Original language	English
Pages (from-to)	1726-1745
Number of pages	20
Journal	Discrete Mathematics
Volume	313
Issue number	17
DOIs	https://doi.org/10.1016/j.disc.2013.04.022
State	Published - 2013

Keywords

Graph
Harmonic
Labeling

All Science Journal Classification (ASJC) codes

Theoretical Computer Science
Discrete Mathematics and Combinatorics

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10.1016/j.disc.2013.04.022

Cite this

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title = "Harmonic labeling of graphs",

abstract = "Which graphs admit an integer valued harmonic function which is injective and surjective onto Zd Such a function, which we call harmonic labeling, is constructed when the graph is the lattice Zd. It is shown that for any finite graph G containing at least one edge, there is no harmonic labeling of G×Z. Further discussion and open problems are presented.",

keywords = "Graph, Harmonic, Labeling",

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year = "2013",

doi = "10.1016/j.disc.2013.04.022",

language = "الإنجليزيّة",

volume = "313",

pages = "1726--1745",

journal = "Discrete Mathematics",

issn = "0012-365X",

publisher = "Elsevier B.V.",

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TY - JOUR

T1 - Harmonic labeling of graphs

AU - Benjamini, Itai

AU - Cyr, Van

AU - Procaccia, Eviatar B.

AU - Tessler, Ran J.

PY - 2013

Y1 - 2013

N2 - Which graphs admit an integer valued harmonic function which is injective and surjective onto Zd Such a function, which we call harmonic labeling, is constructed when the graph is the lattice Zd. It is shown that for any finite graph G containing at least one edge, there is no harmonic labeling of G×Z. Further discussion and open problems are presented.

AB - Which graphs admit an integer valued harmonic function which is injective and surjective onto Zd Such a function, which we call harmonic labeling, is constructed when the graph is the lattice Zd. It is shown that for any finite graph G containing at least one edge, there is no harmonic labeling of G×Z. Further discussion and open problems are presented.

KW - Graph

KW - Harmonic

KW - Labeling

UR - http://www.scopus.com/inward/record.url?scp=84878389009&partnerID=8YFLogxK

U2 - 10.1016/j.disc.2013.04.022

DO - 10.1016/j.disc.2013.04.022

M3 - مقالة

SN - 0012-365X

VL - 313

SP - 1726

EP - 1745

JO - Discrete Mathematics

JF - Discrete Mathematics

IS - 17

ER -

Harmonic labeling of graphs

Abstract

Keywords

All Science Journal Classification (ASJC) codes

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