Note on group distance magic complete bipartite graphs
Sylwia Cichacz
Open Mathematics, Tome 12 (2014), p. 529-533 / Harvested from The Polish Digital Mathematics Library
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A Γ-distance magic labeling of a graph G = (V, E) with |V| = n is a bijection ℓ from V to an Abelian group Γ of order n such that the weight w(x)=∑y∈NG(x)ℓ(y) of every vertex x ∈ V is equal to the same element µ ∈ Γ, called the magic constant. A graph G is called a group distance magic graph if there exists a Γ-distance magic labeling for every Abelian group Γ of order |V(G)|. In this paper we give necessary and sufficient conditions for complete k-partite graphs of odd order p to be ℤp-distance magic. Moreover we show that if p ≡ 2 (mod 4) and k is even, then there does not exist a group Γ of order p such that there exists a Γ-distance labeling for a k-partite complete graph of order p. We also prove that K m,n is a group distance magic graph if and only if n + m ≢ 2 (mod 4).

Publié le : 2014-01-01
EUDML-ID : urn:eudml:doc:269065 
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     author = {Sylwia Cichacz},
     title = {Note on group distance magic complete bipartite graphs},
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     volume = {12},
     year = {2014},
     pages = {529-533},
     zbl = {1284.05122},
     language = {en},
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Sylwia Cichacz. Note on group distance magic complete bipartite graphs. Open Mathematics, Tome 12 (2014) pp. 529-533. http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_2478_s11533-013-0356-z/

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