论文标题
某些顶点加权图的连接的边缘理想
The edge ideals of the join of some vertex weighted oriented graphs
论文作者
论文摘要
在本文中，我们描述了某些图的连接的边缘理想的主要分解，这些信息是每个图形的边缘理想的信息。同时，我们还研究了这种优势理想的符号力量和普通力量的深度和规律性。我们明确计算两个图的连接的边缘理想的普通力的深度和规律性，这些图是由孤立的顶点组成的，还提供了这种边缘理想的符号能力规律性的上限。对于每个图至少一个方向边缘的两个图的连接的边缘理想，我们为它们的深度和规律性提供了确切的公式，还提供了这种边缘理想的普通力量规律性的上限。一些示例表明可以获得这些上限，但可能是严格的。
In this paper, we describe primary decomposition of the edge ideal of the join of some graphs in terms of that information of the edge ideal of every weighted oriented graph. Meanwhile, we also study depth and regularity of symbolic powers and ordinary powers of such an edge ideal. We explicitly compute depth and regularity of ordinary powers of the edge ideal of the join of two graphs consisting of isolated vertices, and also provide upper bounds of regularity of symbolic powers of such an edge ideal. For the edge ideal of the join of two graphs with at least an oriented edge for per graph, we give the exact formulas for their depth and regularity, and also provide the upper bounds of regularity of ordinary powers of such an edge ideal. Some examples show that these upper bounds can be obtained, but may be strict.
