论文标题
在封闭距离的魔术循环器上，价格高达$ 5 $
On closed distance magic circulants of valency up to $5$
论文作者
论文摘要
令$γ=（v，e）$为订单$ n $的图。 $γ$的{\ em封闭式距离魔术标签}是一个两份$ \ ell：v \ to \ to \ {1,2，\ ldots，n \} $，其中存在一个正整数$ r $，因此$ \ sum_ {x \ in N [u]}} \ ell（x）} $ u $。如果图形接收近距离的魔术标签，则据说图形为{\ em封闭距离}。 在本文中，我们将所有连接的封闭距离魔术循环器分类为价值最多5美元，也就是说，Cayley Graphs $ \ operatatorName {cay}（\ Mathbb {z} _n; s）$ where $ | s | \ le 5 $和$ s $生成$ \ mathbb {z} _n $。
Let $Γ=(V,E)$ be a graph of order $n$. A {\em closed distance magic labeling} of $Γ$ is a bijection $\ell : V \to \{1,2, \ldots, n\}$ for which there exists a positive integer $r$ such that $\sum_{x \in N[u]} \ell(x) = r$ for all vertices $u \in V$, where $N[u]$ is the closed neighborhood of $u$. A graph is said to be {\em closed distance magic} if it admits a closed distance magic labeling. In this paper, we classify all connected closed distance magic circulants with valency at most $5$, that is, Cayley graphs $\operatorname{Cay}(\mathbb{Z}_n;S)$ where $|S| \le 5$ and $S$ generates $\mathbb{Z}_n$.
