arXivDaily arXiv每日学术速递 周一至周五更新
arXiv周末暂无论文更新，休息一下吧，周末愉快~~
arXiv 1302.6561math.CO
收藏

群距离幻图$G\times C_n$

Group distance magic graphs $G\times C_n$

Sylwia Cichacz

发表信息：
Discrete Applied Mathematics 177(20) (2014) 80-87
阅读 PDF
arXiv 页面 ↗HTML 原文 ↗

摘要：

图$|V | = n$的$Γ$ -距离魔标号是从$V$到阶为$n$的阿贝尔群$Γ$的双射$f$，使得每个顶点$x \in V$的权重$w(x)=\sum_{y\in N_G(x)}f(y)$等于相同的元素$μ\in Γ$，称为\emph{magic constant}。本文证明了：如果$G$是一个阶为$n=2^{p}(2k+1)$的图，对于某些自然数$p$，$k$，使得对于任何$v\in V(G)$，对于某些常数$c$，有$°(v)\equiv c \imod {2^{p+2}}$，则对于任何阶为$4n$的阿贝尔群$Γ$，对于直积$G\times C_4$，存在$Γ$ -距离幻标号.此外，如果$c$是偶数，则对于直积$G\times C_8$，对于任意阶为$8n$的阿贝尔群$Γ$，存在一个$Γ$ -距离魔标号.

英文摘要：

A $Γ$-distance magic labeling of a graph $G=(V,E)$ with $|V | = n$ is a bijection $f$ from $V$ to an Abelian group $Γ$ of order $n$ such that the weight $w(x)=\sum_{y\in N_G(x)}f(y)$ of every vertex $x \in V$ is equal to the same element $μ\in Γ$, called the \emph{magic constant}. In this paper we will show that if $G$ is a graph of order $n=2^{p}(2k+1)$ for some natural numbers $p$, $k$ such that $°(v)\equiv c \imod {2^{p+2}}$ for some constant $c$ for any $v\in V(G)$, then there exists a $Γ$-distance magic labeling for any Abelian group $Γ$ of order $4n$ for the direct product $G\times C_4$. Moreover if $c$ is even then there exists a $Γ$-distance magic labeling for any Abelian group $Γ$ of order $8n$ for the direct product $G\times C_8$.

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。

↑