正则图的外连通度和外条件诊断之间的关系

林丽美、许力、陈日清*、谢孙源、王大进

    The h-extra node-connectivity of a graph G is the size of a minimal node-set, whose removal will disconnect G, but each remaining component has no fewer h + 1 nodes. Based on h-extra node-connectivity, the h-extra conditional fault-diagnosability of networks has been proposed for a better, more realistic measure of networks’ fault-tolerability. It is the maximal x such that G is h-extra conditionally x-fault-diagnosable. This paper will establish a relationship between the h-extra node-connectivity and h-extra conditional fault-diagnosability for a regular graph G, under the classic PMC diagnostic model. We will apply the newly found relationship to a variety of well-known regular networks, to directly obtain their h-extra conditional fault-diagnosability. The significance of the paper’s work is that it relates the notions of h-extra node-connectivity and h-extra conditional fault-diagnosability, so that a regular network’s h-extra conditional fault-diagnosability may be known once its h-extra node-connectivity is known.

    博士后：林丽美

    单位：福建农林大学计算机与信息学院

    研究领域：网络与信息安全，在图论及其应用方向取得了多项前沿创新成果：提出解决一系列拓扑图故障容错和故障诊断的计算方法和证明策略，突破求解单个拓扑图可靠性的传统方法；建立拓扑图故障容错与故障诊断之间的一般性关系，成功解决拓扑图可靠性中的公开难题；利用拓扑图可靠性研究移动社会网络的优化和安全问题，这与传统研究中仅仅将密码学理论应用于网络安全研究相比，有明显的特色和创新性，为该领域的研究工作提供了一条新途径；探索拓扑图可靠性在复杂生物网络的空间结构稳定性问题的应用，突破架构特性对生物网络的传统影响。本文被国际顶级期刊IEEE Transactions on Dependable and Secure Computing（中国计算机协会CCF推荐的A类期刊）所接收，本人建立了正则图的外连通度和外条件诊断度之间的一般关系，并将这个新发现的关系用到一系列著名的正则网络当中，用来直接获取外条件诊断度。