韧度变种与k-树的连通偶因子

Toughness Variant and Connected Even Factors in k-tree

连通偶[2,2 s]-因子H是G的连通生成子图,且每个顶点在H中的度属于{2,4,…,2s}.韧度变种用于衡量网络的易受攻击程度,是网络拓扑设计的重要指标.给出图存在连通偶[2,2 s]-因子的韧度变种条件,该结论在网络数据传输中有潜在的应用.

Connected even[2,2s]-factor H is a connected spanning subgraph of G,and the degree of each vertex in H belongs to{2,4,…,2s}.The toughness variant is used to measure the vulnerability of the network and is an important indicator of network topology design.In this paper,the toughness variation condition of the existence of connected even[2,2s]-factor in a graph is given.This conclusion has potential applications in network data transmission.