Rupture degree of graphs

被引：64
|
作者：
Li, YK
Zhang, SG [1 ]
Li, XL
机构：
[1] Northwestern Polytech Univ, Dept Math Appl, Xian 710072, Peoples R China
[2] Qinghai Nationalities Coll, Dept Math, Xining 810000, Qinghai, Peoples R China
[3] Nankai Univ, Ctr Combinator, Tianjin 300071, Peoples R China
来源：
INTERNATIONAL JOURNAL OF COMPUTER MATHEMATICS | 2005年 / 82卷 / 07期
基金：
中国国家自然科学基金;
关键词：
network vulnerability; rupture degree; Nordhaus-Gaddum type result;
D O I：
10.1080/00207160412331336062
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
We introduce a new graph parameter, the rupture degree. The rupture degree for a complete graph K,, is defined as 1 - n, and the rupture degree for an incomplete connected graph G is defined by r(G) = max {omega(G - X) - |X| - m(G - X) : X subset of V(G), omega(G - X) > 1}, where omega(G - X) is the number of components of G - X and m(G - X) is the order of a largest component of G - X. It is shown that this parameter can be used to measure the vulnerability of networks. Rupture degrees of several specific classes of graphs are determined. Formulas for the rupture degree of join graphs and some bounds of the rupture degree are given. We also obtain some Nordhaus-Gaddum type results for the rupture degree.
引用
收藏
页码：793 / 803
页数：11
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