Abstract: 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 by[λ'], 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 if[λ'=ξ]. In this paper, some sufficient conditions are presented for networks to be maximally restricted edge-connected.

Key words: interconnection networks, restricted edge cuts, restricted edge connectivity, maximally restricted edge-connected graphs

摘要： 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。

关键词: 互连网络, 限制边割, 限制边连通度, 极大限制边连通图