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

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F61989100%3A27240%2F14%3A86088187" target="_blank" >RIV/61989100:27240/14:86088187 - 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
On Super Vertex-Magic Total Labeling of the Disjoint Union of k Copies of K_n
Original language description
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).
Czech name
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Czech description
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Type
J<sub>x</sub> - Unclassified - Peer-reviewed scientific article (Jimp, Jsc and Jost)
CEP classification
BA - General mathematics
OECD FORD branch
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Publication year
2014
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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