Supermagic Graphs with Many Different Degrees

Kód výsledku v 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>

Nalezeny alternativní kódy

RIV/61989100:27740/21:10243571

Výsledek na webu

<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>

Jazyk výsledku

angličtina

Název v původním jazyce

Supermagic Graphs with Many Different Degrees

Popis výsledku v původním jazyce

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&apos;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.

Název v anglickém jazyce

Supermagic Graphs with Many Different Degrees

Popis výsledku anglicky

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&apos;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.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10100 - Mathematics

Projekt

<a href="/cs/project/LQ1602" target="_blank" >LQ1602: IT4Innovations excellence in science</a><br>

Návaznosti

P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)<br>S - Specificky vyzkum na vysokych skolach

Rok uplatnění

2021

Kód důvěrnosti údajů

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

Název periodika

Discussiones Mathematicae Graph Theory

ISSN

1234-3099

e-ISSN

—

Svazek periodika

41

Číslo periodika v rámci svazku

4

Stát vydavatele periodika

PL - Polská republika

Počet stran výsledku

10

Strana od-do

1041-1050

Kód UT WoS článku

000667233200010

EID výsledku v databázi Scopus

2-s2.0-85068768749