论文标题
在远程魔术循环器上6
On distance magic circulants of valency 6
论文作者
论文摘要
$ n $的图$γ=（v，e）$是{\ em远程魔术}，如果它承认了$ \ ell \ el \ colon v \ to \ {1,2，\ ldots，n \} $的c \ el \ ell \ colon v \ to \ ldots，n \} $，存在一个正integer $κ$κ$ \ um \ sum_ el \ ul）对于所有顶点$ v \ in V $，其中$ n（v）$是$ v $的邻里。 ％众所周知，常规距离魔术图一定具有甚至价值。 一个{\ em循环}是一个图表，该图周期为自动形态，将其顶点置换。在本文中，我们研究了距离价值$ 6 $的远程魔术循环器。我们获得了一些必要的和一些足够的条件，可以使价值$ 6 $的循环系统成为远程魔术，从而找到了几个无限的示例家庭。本文的综合结果提供了所有距离的魔术循环器$ 6 $的部分分类。特别是，我们将价值远距离循环器分类为$ 6 $，其订单不可划分$ 12 $。
A graph $Γ= (V,E)$ of order $n$ is {\em distance magic} if it admits a bijective labeling $\ell \colon V \to \{1,2, \ldots, n\}$ of its vertices for which there exists a positive integer $κ$ such that $\sum_{u \in N(v)} \ell(u) = κ$ for all vertices $v \in V$, where $N(v)$ is the neighborhood of $v$. %It is well known that a regular distance magic graph is necessarily of even valency. A {\em circulant} is a graph admitting an automorphism cyclically permuting its vertices. In this paper we study distance magic circulants of valency $6$. We obtain some necessary and some sufficient conditions for a circulant of valency $6$ to be distance magic, thereby finding several infinite families of examples. The combined results of this paper provide a partial classification of all distance magic circulants of valency $6$. In particular, we classify distance magic circulants of valency $6$, whose order is not divisible by $12$.
