论文标题
广义图花键和通用差异属性
Generalized graph splines and the Universal Difference Property
论文作者
论文摘要
我们研究了Gilbert，Tymoczko和Viel引入的广义图样条纹，并专注于称为通用差异特性（UDP）的属性。我们证明路径，树木和周期满足UDP。我们在粘贴在单个顶点粘贴的图形上探索UDP，并使用prüfer域来说明并非每个边缘图形都满足UDP。我们表明，当$ r $是prüfer域时，UDP必须保留在环$ r $上的任何边缘图。最后，我们证明UDP是通过带有边缘图的同构保留的。
We study the generalized graph splines introduced by Gilbert, Tymoczko, and Viel and focus on an attribute known as the Universal Difference Property (UDP). We prove that paths, trees, and cycles satisfy UDP. We explore UDP on graphs pasted at a single vertex and use Prüfer domains to illustrate that not every edge labeled graph satisfies UDP. We show that UDP must hold for any edge labeled graph over a ring $R$ if and only if $R$ is a Prüfer domain. Lastly, we prove that UDP is preserved by isomorphisms of edge labeled graphs.
