论文标题
pertfect匹配和零和3麦克数标签
Pertfect matching and zero-sum 3-magic labeling
论文作者
论文摘要
映射$ l：e（g）\ rightarrow a $，其中$ a $是一个阿贝尔集团，添加性地写着图$ g $的标签。对于每个正整数$ h \ geqslant 2 $，如果有一个边缘标记$ e（g）$的$ l $ to $ e（g）到$ \ mathbb {z} _ {z} _ {h} _ {h} _ {h} \ backslash \ backslash \ fackslash \ \ \ \ c {0 \} $ s un $ e（g）} l（uv）= 0 $ in V（g）$中的每个顶点$ v \。 2014年，Saieed Akbari，Farhad Rahmati和Sanaz Zare猜想，每5个款式的图表都承认零3 $ 3 $ - 玛吉的标签。在本文中，我们获得的是，每个边缘都包含每个边缘的每5个型图必须具有完美的匹配，并且承认一个零和3-MAGIC标签，这部分确认了这一猜想。
A mapping $l : E(G) \rightarrow A$, where $A$ is an abelian group which written additively, is called a labeling of the graph $G$. For every positive integer $h \geqslant 2$, a graph $G$ is said to be zero-sum $h$-magic if there is an edge labeling $l$ from $E(G)$ into $\mathbb{Z}_{h} \backslash \{0\}$ such that $s(v) = \sum_{uv\in E(G)}l(uv) = 0$ for every vertex $v \in V(G)$. In 2014, Saieed Akbari, Farhad Rahmati and Sanaz Zare conjectured that every 5-regular graph admits a zero-sum $3$-magic labeling. In this paper, we obtained that every 5-regular graph with every edge contains in a triangle must have a perfect matching, and admits a zero-sum 3-magic labeling, which partially confirms this conjecture.
