摘要
研究了1-型三圈图和2-型三圈图的正负惯性指数和零度问题.通过删除悬挂的树和压缩内部路等方法,给出这两类特殊三圈图的正负惯性指数和零度的计算方法,得到以下结论:1-型三圈图的正负惯性指数(或零度)等于一些树和一些双圈图的正负惯性指数(或零度)之和;2-型三圈图的正负惯性指数(或零度)等于一些树和一些简单三圈图的正负惯性指数(或零度)之和,其中涉及的这些简单三圈图的正负惯性指数和零度可以利用Matlab软件计算;对1-型三圈图和2-型三圈图验证了前人提出的关于图的正负惯性指数差的一个猜想成立.
The problem how to calculate the positive and negative inertia indexes and nullity of one-type and two-type tricyclic graphs are studied. By means of deleting pendant trees and compressing internal paths, a method of calculating the positive and negative inertia indexes and nullity of the two special kinds of tricyclic graphs are given. It is proved that the positive and negative inertia indexes and nullity of one-type tricyclic graphs equal to the sum of those of some trees and bicyclic graphs, respectively; the positive and negative inertia indexes and nullity of two-type tricyclic graphs equal to the sum of those of some trees and simple tricyclic graphs respectively; the positive and negative inertia indexes and nullity of these simple tricyclic graphs can be calculated by Matlab. For one-type and two-type tricyclic graphs, a conjecture about difference of the positive and negative inertia index of a graph is verified.
出处
《陕西师范大学学报（自然科学版）》
CAS
CSCD
北大核心
2013年第4期16-19,共4页
Journal of Shaanxi Normal University：Natural Science Edition
基金
国家自然科学基金资助项目(11071151)
陕西省自然科学基金资助项目(2010JM1005)
陕西师范大学研究生培养创新基金项目(2013CXS025)
关键词
三圈图
正惯性指数
负惯性指数
零度
tricyclic graph
positive inertia index
negative inertia index
nullity
