任意图上的广义双样条
Generalized Integer Splines on Arbitrary Graphs
摘要：
图$G$上的具有整数边权的广义整数样条是整数顶点标号，使得如果$G$中的两个顶点共享一条边，则顶点标号模边权是全等的。我们引入折叠操作，减少任何单图到一个单一的顶点，携带它的边的重量信息。这对应于一个序列的满射映射之间的相关样条模块，导致一个明确的建设一个模块的基础上的边缘权重。
英文摘要：
Generalized integer splines on a graph $G$ with integer edge weights are integer vertex labelings such that if two vertices share an edge in $G$, the vertex labels are congruent modulo the edge weight. We introduce collapsing operations that reduce any simple graph to a single vertex, carrying with it the edge weight information. This corresponds to a sequence of surjective maps between the associated spline modules, leading to an explicit construction of a module basis in terms of the edge weights.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
