中文摘要：

令G是一个2-边连通简单图,且阶数n≥11,令A是一个单位元为0的阿贝尔群.重复收缩图G的非平凡A-连通子图,直到没有这样的子图,所得的新图记为G＊,则称G可以A-收缩到G＊.文中证明了如果图G满足δ（G）n≤「n/3」-1且对uvE（G）,有｜N（v）∪N（u）2n｜≥「2n/3」-1,那么G不是Z33-连通图当且仅当G可Z3-收缩到{C3,K4,K-4,L}中的一个,其中L是在K4上加一个新点,并且此新点与K4连两条边所得到的简单图.

英文摘要：

Let G be a 2- edge connected simple graph with n≥11,and A be an abelian group with identity 0.We say that G can be A-reduced to G＊,if G＊is obtained by repeatedly contracting nontrivial A-connected subngraphs until no such a subgraph is left. In this paper,we prove that if δ（G）n≤「n/3」-1 and for uvE（G）,｜N（v）∪N（u）2n｜≥「2n/3」-1,then G is not Zd if and only if G can be Z33-connecte 3-reduced to one of { C3,K4,K-4,L},where L is obtained from K4 by adding a new vertex which is joined to two vertices of K4.