图的边韧性度(英文)

Edge-Tenacity in Graphs

中文关键词:  边割集  严格边韧性度图  K-树  较高阶的边坚韧度  边坚韧度

英文关键词:edge cut-sets  strictly edge-tenacious graph  K-trees  higher-order edge toughness  edge toughness.

中文摘要:

      文[1]中,定义图G(V,E)的边韧性度定义为min{(|S|+T(G-S))/(ω(G-S)):S?E(G)},这里,T-(G-S)和ω(G-S)分别表示G-S中最大分支的顶点数和连通分支数.这是一个能衡量网络图稳定性较好的参数,因为它不仅考虑到了图G-S的分支数也考虑到了它的阶数.在以前的工作中,作者得到了边韧性度图的一个充要条件.利用这些结果证明了K-树是严格边韧性度图,并找到了边韧性度与较高阶的边坚韧度和边坚韧度之间的关系.

英文摘要:

      The edge-tenacity of a graph G(V,E) is denned as min{(|S|+T(G-S))/(ω(G-S)):S?E(G)},where T(G-S) and ω(G-S), respectively, denote the order of the largest component and the number of the components of G-S. This is a better parameter to measure the stability of a network G, as it takes into account both the quantity and the order of components of the graph G-S. In a previous work, we established a necessary and sufficient condition for a graph to be edge-tenacious. These results are applied to prove that K-trees are strictly edge-tenacious. A number of results are given on the relation of edge-tenacity and other parameters, such as the higher-order edge toughness and the edge-toughness.