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Electronic Notes in Discrete Mathematics
Article . 2013 . Peer-reviewed
License: Elsevier TDM
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Distance magic labelings of hypercubes

Authors: Petr Gregor; Petr Kovár;

Distance magic labelings of hypercubes

Abstract

Abstract A distance magic labeling of a graph G is a bijective assignment of labels from {1, 2, …, |V (G)|} to the vertices of G such that the sum of labels on neighbors of u is the same for all vertices u. We show that the n-dimensional hypercube has a distance magic labeling for every n ≡ 2 ( mod 4 ) . It is known that this condition is also necessary. This completes solution of a conjecture posed by Acharya et al. [B. D. Acharya, S. B. Rao, T. Singh and V. Parameswaran, Neighborhood magic graphs, In National Conference on Graph Theory, Combinatorics and Algorithm, 2004].

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selected citations
These citations are derived from selected sources.
This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Citations provided by BIP!
popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
BIP!Impulse provided by BIP!
5
Top 10%
Top 10%
Average
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