Computer Engineering and Applications ›› 2017, Vol. 53 ›› Issue (8): 19-22.DOI: 10.3778/j.issn.1002-8331.1611-0026

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Sufficient conditions for networks to be maximally restricted edge-connected

ZHANG Guozhen   

  1. School of Mathematical Sciences, Shanxi University, Taiyuan 030006, China
  • Online:2017-04-15 Published:2017-04-28

极大限制边连通网络的充分条件

张国珍   

  1. 山西大学 数学科学学院,太原 030006

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