图是λ_5-最优的邻域交条件

Neighborhood Intersection Conditions for λ_5-Optimality in Graphs

基于目前网络边连通性在网络拓扑性能方面的广泛应用和高阶限制边通图的各种邻域条件的广泛关注,针对图的高阶限制边连通性的最优化问题进行了深入的研究。该结论通过运用分类讨论和反证假设的方法,对前人一些已知的结果进行推广和改进,给出了阶为n的λ5-连通图的邻域交条件,从而得出图是λ5-最优的充分性条件。这些结论在大规模网络系统中度量网络性能的可靠性和容错性分析方面都有一定的应用,并对研究更高阶的网络连通性的最优化问题提供了方法和理论依据。

Based on the current network edge connectivity in the network topology of the extensive application and the restricted edge through diagrams of various neighborhood conditions for graphs widely attention,the high-order restricted edge connectivity of the optimization problems are studied.By using the classification and disproof of thought,some previous known results are improved and extended,the order which is n to the λ5-connected graph neighborhood intersection condition is given so that the optimal sufficient conclusions are deduced.These conclusions in the reliability analysis and fault-tolerance of network have certain application,and provide certain methods and theoretical basis for the research of higher-order connectivity optimization problem.