Magic labelings of regular graphs

Result code in IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F61989100%3A27240%2F07%3A00015141" target="_blank" >RIV/61989100:27240/07:00015141 - isvavai.cz</a>

Result on the web

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DOI - Digital Object Identifier

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Result language

angličtina

Original language name

Magic labelings of regular graphs

Original language description

Let G(V,E) be a graph and ? be a bijection from the set V or E to the set of the first |V|+|E| natural numbers. The weight of a vertex is the sum of its label and the labels of all adjacent edges. We say ? is a vertex magic total (VMT) labeling of G if the weight of each vertex is constant. We say ? is an (s,d)-vertex antimagic total (VAMT) labeling if the vertex weights form an arithmetic progression starting at s with difference d. J. MacDougall conjectured that any regular graph with the exception ofK2 and 2K3 has a VMT labeling. We give constructions of VAMT labelings of any even-regular graphs and VMT labelings of certain regular graphs.

Czech name

Magic labelings of regular graphs

Czech description

Let G(V,E) be a graph and ? be a bijection from the set V or E to the set of the first |V|+|E| natural numbers. The weight of a vertex is the sum of its label and the labels of all adjacent edges. We say ? is a vertex magic total (VMT) labeling of G if the weight of each vertex is constant. We say ? is an (s,d)-vertex antimagic total (VAMT) labeling if the vertex weights form an arithmetic progression starting at s with difference d. J. MacDougall conjectured that any regular graph with the exception ofK2 and 2K3 has a VMT labeling. We give constructions of VAMT labelings of any even-regular graphs and VMT labelings of certain regular graphs.

Type

J_x - Unclassified - Peer-reviewed scientific article (Jimp, Jsc and Jost)

CEP classification

BA - General mathematics

OECD FORD branch

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Project

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Continuities

Z - Vyzkumny zamer (s odkazem do CEZ)

Publication year

2007

Confidentiality

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Name of the periodical

AKCE International Journal of Graphs and Combinatorics

ISSN

0972-8600

e-ISSN

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Volume of the periodical

4

Issue of the periodical within the volume

3

Country of publishing house

IN - INDIA

Number of pages

16

Pages from-to

261-275

UT code for WoS article

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EID of the result in the Scopus database

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