On zero sum-partition of Abelian groups into three sets and group distance magic labeling

IF 0.6 3区 数学 Q3 MATHEMATICS Ars Mathematica Contemporanea Pub Date : 2017-05-09 DOI:10.26493/1855-3974.1054.FCD
S. Cichacz
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引用次数: 8

Abstract

We say that a finite Abelian group Γ  has the constant-sum-partition property into t sets (CSP ( t ) -property) if for every partition n  =  r 1  +  r 2  + … +  r t of n , with r i  ≥ 2 for 2 ≤  i  ≤  t , there is a partition of Γ  into pairwise disjoint subsets A 1 ,  A 2 , …,  A t , such that ∣ A i ∣ =  r i and for some ν  ∈ Γ  , ∑  a  ∈  A i a  =  ν for 1 ≤  i  ≤  t . For ν  =  g 0 (where g 0 is the identity element of Γ  ) we say that Γ  has zero-sum-partition property into t sets (ZSP ( t ) -property). 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  ∈  N ( 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 study the CSP (3) -property of Γ  , and apply the results to the study of group distance magic complete tripartite graphs.
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阿贝尔群的零和划分及群距幻标
我们说一个有限阿贝尔群Γconstant-sum-partition属性为t集(CSP (t)财产)如果为每个分区n = 1 + r 2  + ... +  r t (n, 2 r≥2≤≤t,我有一个分区Γ两两不相交的子集1,2,…,t,这样∣我∣= r和一些ν∈Γ,∑∈一我=ν1≤≤t。对于ν = g 0(其中g 0是Γ的单位元),我们说Γ具有零和划分属性,分为t个集合(ZSP (t) -属性)。图G = (V, E),∣V∣= n的Γ -距离幻标号是一个从V到n阶阿贝尔群Γ的双射l,使得每个顶点x∈V的权w (x) =∑y∈n (x) l(y)等于同一个元素μ∈Γ,称为幻常数。如果对于每个阶为∣V (G)∣的阿别群Γ存在一个Γ -距离幻标,则图G称为群距离幻图。本文研究了Γ的CSP(3) -性质,并将结果应用于群距离幻完全三部图的研究。
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来源期刊
Ars Mathematica Contemporanea
Ars Mathematica Contemporanea MATHEMATICS, APPLIED-MATHEMATICS
CiteScore
1.70
自引率
0.00%
发文量
45
审稿时长
>12 weeks
期刊介绍: Ars mathematica contemporanea will publish high-quality articles in contemporary mathematics that arise from the discrete and concrete mathematics paradigm. It will favor themes that combine at least two different fields of mathematics. In particular, we welcome papers intersecting discrete mathematics with other branches of mathematics, such as algebra, geometry, topology, theoretical computer science, and combinatorics. The name of the journal was chosen carefully. Symmetry is certainly a theme that is quite welcome to the journal, as it is through symmetry that mathematics comes closest to art.
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