中文摘要：

设G是有限简单无向图，使G—S每个分支的阶至少为4的边割S称为G的4阶限制边割．G的4阶限制边连通度λ4（G）是G的4阶限制边割之中最少的边数，达到最小的叫λ4边割．定义ξ4（G）=min{ （U）：UCV（G），G[U]是4阶连通子图}，此处 （U）表示恰好有一个端点在U中的边数．若λ4（G）=ξ4（G），则称G是λ4最优的．若任意λ4边割都孤立一个4阶连通子图，则称G是超级λ4连通的．给出图是λ4最优和超级v4连通的度条件，并举例说明条件的最好可能性．

英文摘要：

Let G be a finite, simple and undirected graph. An edge-cut S of G is 4-restricted if each component of G -S contains at least 4 vertices. The 4-restricted edge connectivity of G, denoted as λ4（G）, is defined as the minimum cardinality of all 4-restricted edge-cuts, and the minimum ones are called λ4-edge-cuts. Let ξ4 （G） = min{ （U） ： UC V（G）, G[ U] is a connected subgraph of order 4 of G,where O（U） denotes the edge number exactly having one endvertex in U. A graph is λ4- optimal if λ4-（G） =ξ4 （G）. A graph is super-λ4 if every λ4- edge-cut isolates a connected subgraph of order 4. This paper presents degree conditions super-λ4. Moreover, this paper gives some cases possible. for a graph to be λ4- optimal and a graph to be to demonstrate that these conditions are the most possible.