On Super Vertex-Magic Total Labeling of the Disjoint Union of k Copies of K_n

Kód výsledku v IS VaVaI

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Výsledek na webu

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DOI - Digital Object Identifier

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Jazyk výsledku

angličtina

Název v původním jazyce

On Super Vertex-Magic Total Labeling of the Disjoint Union of k Copies of K_n

Popis výsledku v původním jazyce

Let G = (V, E) be a finite non-empty graph. A vertex-magic total labeling (VMTL) is a bijection lambda from V boolean OR E to the set of consecutive integers {1, 2,..., |V|+|E|} with the property that for every v is an element of V, lambda(v) + Sigma w is an element of N(v) lambda(vw) = h, for some constant h. Such a labeling is called super if the vertex labels are 1, 2,..., |V|. There are some results known about super VMTL of kG only when the graph G has a super VMTL. In this paper we focus on the case when G is the complete graph K-n. It was shown that a super VMTL of kK(n) exists for n odd and any k, for 4 < n equivalent to 0 (mod 4) and any k, and for n = 4 and k even. We continue the study and examine the graph kK(n) for n equivalent to 2 (mod 4). Let n = 4l + 2 for a positive integer l. The graph kK(4l+2) does not admit a super VMTL for k odd. We give a large number of super VMTLs of kK(4l+2) for any even k based on super VMTL of 4K(2l+1).

Název v anglickém jazyce

On Super Vertex-Magic Total Labeling of the Disjoint Union of k Copies of K_n

Popis výsledku anglicky

Let G = (V, E) be a finite non-empty graph. A vertex-magic total labeling (VMTL) is a bijection lambda from V boolean OR E to the set of consecutive integers {1, 2,..., |V|+|E|} with the property that for every v is an element of V, lambda(v) + Sigma w is an element of N(v) lambda(vw) = h, for some constant h. Such a labeling is called super if the vertex labels are 1, 2,..., |V|. There are some results known about super VMTL of kG only when the graph G has a super VMTL. In this paper we focus on the case when G is the complete graph K-n. It was shown that a super VMTL of kK(n) exists for n odd and any k, for 4 < n equivalent to 0 (mod 4) and any k, and for n = 4 and k even. We continue the study and examine the graph kK(n) for n equivalent to 2 (mod 4). Let n = 4l + 2 for a positive integer l. The graph kK(4l+2) does not admit a super VMTL for k odd. We give a large number of super VMTLs of kK(4l+2) for any even k based on super VMTL of 4K(2l+1).

Druh

J_x - Nezařazeno - Článek v odborném periodiku (Jimp, Jsc a Jost)

CEP obor

BA - Obecná matematika

OECD FORD obor

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Projekt

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Návaznosti

Z - Vyzkumny zamer (s odkazem do CEZ)

Rok uplatnění

2014

Kód důvěrnosti údajů

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

Název periodika

Ars Combinatoria

ISSN

0381-7032

e-ISSN

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Svazek periodika

2014

Číslo periodika v rámci svazku

113

Stát vydavatele periodika

CA - Kanada

Počet stran výsledku

18

Strana od-do

175-192

Kód UT WoS článku

000329883500015

EID výsledku v databázi Scopus

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