极大限制边连通网络的充分条件

限制边连通度是度量网络可靠性的重要参数。设G]是一个边集为E]的连通网络。称一个边集合S?E]是一个限制边割，如果G-S]是不连通的且每个分支至少有两个顶点。网络G]的限制边连通度，记为λ']，定义为G]的最小限制边割的基数。设d(v)]表示顶点v]的度，ξ=min{d(u)+d(v)-2:uv∈E}]表示G]的最小边度。称网络G]是极大限制边连通的，如果λ'=ξ]。给出了网络是极大限制边连通的一些充分条件。

Sufficient conditions for networks to be maximally restricted edge-connected

The restricted edge connectivity is an important index to measure the reliability of networks. For a connected network G] with edge set E], an edge set S?E] is a restricted edge cut if G-S] is disconnected and every component of G-S] has at least two vertices. The restricted edge connectivity of G], denoted byλ'], is defined as the cardinality of a minimum restricted edge cut. Let d(v)] be the degree of a vertex v] and let ξ=min{d(u)+d(v)-2:uv∈E}] be the minimum edge degree of G]. A connected network G] is maximally restricted edge-connected ifλ'=ξ]. In this paper, some sufficient conditions are presented for networks to be maximally restricted edge-connected.