Edge-Tenacity in Graphs  

图的边韧性度(英文)

作　　者：王志平[1] 任光[2] 赵连昌[1] 

机构地区：[1]大连海事大学数理系,辽宁大连116026 [2]大连海事大学轮机工程学院,辽宁大连116026

出　　处：《Journal of Mathematical Research and Exposition》2004年第3期405-410,共6页数学研究与评论（英文版）

基　　金：SuppoSed by the Ministry of Communication(200332922505); the Doctoral Foundation of Ministry of Education(20030151005)

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.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.

关 键 词：edge cut-sets strictly edge-tenacious graph K-trees higher-order edge toughness edge toughness. 

分 类 号：O157.5[理学—数学]