Supermagic Graphs with Many Different Degrees
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F61989100%3A27240%2F21%3A10243571" target="_blank" >RIV/61989100:27240/21:10243571 - isvavai.cz</a>
Alternative codes found
RIV/61989100:27740/21:10243571
Result on the web
<a href="https://www.dmgt.uz.zgora.pl/publish/view_press.php?ID=7195" target="_blank" >https://www.dmgt.uz.zgora.pl/publish/view_press.php?ID=7195</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.7151/dmgt.2227" target="_blank" >10.7151/dmgt.2227</a>
Alternative languages
Result language
angličtina
Original language name
Supermagic Graphs with Many Different Degrees
Original language description
Let G = (V, E) be a graph with n vertices and e edges. A supermagic labeling of G is a bijection f from the set of edges E to a set of consecutive integers {a, a + 1, ..., a + e - 1} such that for every vertex v ϵ V the sum of labels of all adjacent edges equals the same constant k. This k is called a magic constant of f, and G is a supermagic graph. The existence of supermagic labeling for certain classes of graphs has been the scope of many papers. For a comprehensive overview see Gallian's Dynamic survey of graph labeling in the Electronic Journal of Combinatorics. So far, regular or almost regular graphs have been studied. This is natural, since the same magic constant has to be achieved both at vertices of high degree as well as at vertices of low degree, while the labels are distinct consecutive integers. The question of the existence of highly irregular supermagic graphs had remained open. In this paper we give a positive answer: the degree difference of a supermagic graph can be arbitrarily high. Moreover, we show that the composition G[Kn] is supermagic for every supermagic graph G and odd n.
Czech name
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Czech description
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Classification
Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
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OECD FORD branch
10100 - Mathematics
Result continuities
Project
<a href="/en/project/LQ1602" target="_blank" >LQ1602: IT4Innovations excellence in science</a><br>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)<br>S - Specificky vyzkum na vysokych skolach
Others
Publication year
2021
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
Discussiones Mathematicae Graph Theory
ISSN
1234-3099
e-ISSN
—
Volume of the periodical
41
Issue of the periodical within the volume
4
Country of publishing house
PL - POLAND
Number of pages
10
Pages from-to
1041-1050
UT code for WoS article
000667233200010
EID of the result in the Scopus database
2-s2.0-85068768749