论文标题
龙虾的反吸引力取向
Antimagic orientation of lobsters
论文作者
论文摘要
令$ m \ ge 1 $为整数，$ g $是$ m $边缘的图。我们说$ g $如果$ g $具有方向$ d $和BAIPATION $τ：a（d）\ rightarrow \ {1,2，\ cdots，m \} $，以至于$ d $中没有两个$ d $ $τ$ un的$ d $ d $ d $ d $ um的$ d $ d $ univer的两个顶点，在所有输入$ u $的弧中，所有弧线的标签总和留出了$ u $。 Hefetz，Mütze和Schwartz [J。图理论，64：219-232，2010]猜想，每个连接的图都允许抗原方向。确认了某些类别的图表，例如密集的图，常规图和树木，包括毛毛虫和$ k $ - $ - yr-are Trees。在本说明中，我们证明每个龙虾都承认一个反刺激方向。
Let $m\ge 1$ be an integer and $G$ be a graph with $m$ edges. We say that $G$ has an antimagic orientation if $G$ has an orientation $D$ and a bijection $τ:A(D)\rightarrow \{1,2,\cdots,m\}$ such that no two vertices in $D$ have the same vertex-sum under $τ$, where the vertex-sum of a vertex $u$ in $D$ under $τ$ is the sum of labels of all arcs entering $u$ minus the sum of labels of all arcs leaving $u$. Hefetz, Mütze and Schwartz [J. Graph Theory, 64: 219-232, 2010] conjectured that every connected graph admits an antimagic orientation. The conjecture was confirmed for certain classes of graphs such as dense graphs, regular graphs, and trees including caterpillars and $k$-ary trees. In this note, we prove that every lobster admits an antimagic orientation.
