论文标题
最低度至少33的图形的抗刺激取向
Antimagic orientation of graphs with minimum degree at least 33
论文作者
论文摘要
An antimagic labeling of a directed graph $D$ with $n$ vertices and $m$ arcs is a bijection from the set of arcs of $D$ to the integers $\{1, \cdots, m\}$ such that all $n$ oriented vertex sums are pairwise distinct, where an oriented vertex sum is the sum of labels of all arcs entering that vertex minus the sum of所有弧的标签都离开了。图形$ g $具有抗原方向，如果其具有抗刺激标签的方向。 Hefetz，m {ü} tze，Schwartz猜想每个连接的图都允许抗原方向。在本文中，我们表明，每个没有孤立和度2顶点的两分图都可以接受反刺激方向，并且每个图$ g $均以$δ（g）\ ge 33 $允许抗原方向。我们的证明依赖于新开发的两分图的结构性特性，这可能具有独立的兴趣。
An antimagic labeling of a directed graph $D$ with $n$ vertices and $m$ arcs is a bijection from the set of arcs of $D$ to the integers $\{1, \cdots, m\}$ such that all $n$ oriented vertex sums are pairwise distinct, where an oriented vertex sum is the sum of labels of all arcs entering that vertex minus the sum of labels of all arcs leaving it. A graph $G$ has an antimagic orientation if it has an orientation which admits an antimagic labeling. Hefetz, M{ü}tze, and Schwartz conjectured that every connected graph admits an antimagic orientation. In this paper, we show that every bipartite graph without both isolated and degree 2 vertices admits an antimagic orientation and every graph $G$ with $δ(G)\ge 33$ admits an antimagic orientation. Our proof relies on a newly developed structural property of bipartite graphs, which might be of independent interest.
