具有少量平凡特征理想的图
Graphs with few trivial characteristic ideals
摘要：
给出了至多具有三个平凡特征理想的图的一个刻划。这意味着临界群最多有3个不变因子等于1的正则图的完全刻画和Smith群最多有3个不变因子等于1的图的刻画。给出了Smith群至多有3个不变因子等于1的图的一种可供选择的简单刻画方法，以及Smith群至多有4个不变因子等于1的图族的最小禁止图列表.
英文摘要：
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.
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。
