Czasopismo
Tytuł artykułu
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Warianty tytułu
Języki publikacji
Abstrakty
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 $$w(x) = \sum\nolimits_{y \in N_G (x)} {\ell (y)}$$ 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).
Słowa kluczowe
Kategorie tematyczne
Wydawca
Czasopismo
Rocznik
Tom
Numer
Strony
529-533
Opis fizyczny
Daty
wydano
2014-03-01
online
2013-12-21
Twórcy
Bibliografia
- [1] Arumugam S., Froncek D., Kamatchi N., Distance magic graphs¶a survey, J. Indones. Math. Soc., 2011, Special edition, 11–26
- [2] Beena S., On Σ and Σ′ labelled graphs, Discrete Math., 2009, 309(6), 1783–1787 http://dx.doi.org/10.1016/j.disc.2008.02.038
- [3] Cichacz S., Note on group distance magic graphs G[C 4], Graphs Combin. (in press), DOI: 10.1007/s00373-013-1294-z
- [4] Combe D., Nelson A.M., Palmer W.D., Magic labellings of graphs over finite abelian groups, Australas. J. Combin., 2004, 29, 259–271
- [5] Froncek D., Group distance magic labeling of Cartesian product of cycles, Australas. J. Combin., 2013, 55, 167–174
- [6] Kaplan G., Lev A., Roditty Y., On zero-sum partitions and anti-magic trees, Discrete Math., 2009, 309(8), 2010–2014 http://dx.doi.org/10.1016/j.disc.2008.04.012
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.doi-10_2478_s11533-013-0356-z