论文标题
单车图的边缘理想的符号缺陷
Symbolic defects of edge ideals of unicyclic graphs
论文作者
论文摘要
我们介绍了图中诱导子图的最小边缘盖的概念。令$ g $为具有唯一奇数的独立图形，而$ i = i（g）$是其优势。我们使用图形中诱导子图的最小边缘盖的概念来计算$ i $的所有符号缺陷的确切值。我们描述了一种方法，可以找到与Edge Idend $ i $的符号缺陷相关的准多项式。当任何固定的$ s $的最大理想能力消灭了$ i^{（s）}/i^s $时，我们将Unicclic图的类别分类。同样对于那些图表，我们计算模块的Hilbert函数$ i^{（s）}/i^s $用于所有$s。$。
We introduce the concept of minimum edge cover for an induced subgraph in a graph. Let $G$ be a unicyclic graph with a unique odd cycle and $I=I(G)$ be its edge ideal. We compute the exact values of all symbolic defects of $I$ using the concept of minimum edge cover for an induced subgraph in a graph. We describe one method to find the quasi-polynomial associated with the symbolic defects of edge ideal $I$. We classify the class of unicyclic graphs when some power of maximal ideal annihilates $ I^{(s)}/I^s $ for any fixed $ s $. Also for those class of graphs, we compute the Hilbert function of the module $I^{(s)}/I^s$ for all $s.$
