毛毛虫有反魔法取向
Caterpillars Have Antimagic Orientations
摘要：
有向图$D$与$m$弧的反魔术标号是从$D$的弧集合到$\{1,\dots,m\}$的双射，使得$D$中的顶点的所有定向顶点和是成对不同的，其中顶点$u$的定向顶点和是进入$u$的所有弧的标号之和减去离开$u$的所有弧的标号之和。Hefetz，Mütze，and Schwartz证明了每个连通图都有一个反魔定向，其中图$G$的反魔定向是图$G$有反魔标记的定向.我们使用建设性的技术来证明，毛毛虫，一个著名的子类的树木，有antimagic的方向。
英文摘要：
An antimagic labeling of a directed graph $D$ with $m$ arcs is a bijection from the set of arcs of $D$ to $\{1,\dots,m\}$ such that all oriented vertex sums of vertices in $D$ are pairwise distinct, where the oriented vertex sum of a vertex $u$ is the sum of labels of all arcs entering $u$ minus the sum of labels of all arcs leaving $u$. Hefetz, Mütze, and Schwartz conjectured that every connected graph admits an antimagic orientation, where an antimagic orientation of a graph $G$ is an orientation of $G$ which has an antimagic labeling. We use a constructive technique to prove that caterpillars, a well-known subclass of trees, have antimagic orientations.
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