论文标题
具有少量琐碎特征理想的图形
Graphs with few trivial characteristic ideals
论文作者
论文摘要
我们给出图形的表征，最多可以具有三个微不足道的特征理想。这意味着普通图的完整表征，其关键组最多具有等于1的不变因素以及史密斯组最多3个不变因素等于1的图表的表征。我们还提供了一种替代，更简单的方法，以获得图形的表征，其史密斯组最多3个不变因子的smith群体最多等于1的不变因素，并且是史密斯的一家图形列表，而史密斯的图形则是史密斯的一家人的列表。
We give a characterization of the graphs with at most three trivial characteristic ideals. This implies the complete characterization of the regular graphs whose critical groups have at most three invariant factors equal to 1 and the characterization of the graphs whose Smith groups have at most 3 invariant factors equal to 1. We also give an alternative and simpler way to obtain the characterization of the graphs whose Smith groups have at most 3 invariant factors equal to 1, and a list of minimal forbidden graphs for the family of graphs with Smith group having at most 4 invariant factors equal to 1.
