两类特殊三圈图的正负惯性指数和零度

doi:10.6040/j.issn.1671-9352.0.2014.267

山东大学学报（理学版） ›› 2015, Vol. 50 ›› Issue (02): 32-37.doi: 10.6040/j.issn.1671-9352.0.2014.267

两类特殊三圈图的正负惯性指数和零度

杨陈, 马海成

青海民族大学数学系, 青海西宁 810007

收稿日期:2014-06-11 修回日期:2014-10-14 出版日期:2015-02-20 发布日期:2015-01-27
作者简介:杨陈(1989-),女,硕士,研究方向为组合数学. E-mail:yangchenmylv@163.com;马海成(1965-),男,教授,研究方向为代数图论. E-mail:qhmymhc@163.com
基金资助:
青海省自然科学基金资助项目(2011-Z-911)

Positive and negative inertia indexes and nullity of two special kinds of tricyclic graphs

YANG Chen, MA Hai-cheng

Department of Mathematics, Qinghai University for Nationalities, Xining 810007, Qinghai, China

Received:2014-06-11 Revised:2014-10-14 Online:2015-02-20 Published:2015-01-27

摘要/Abstract

摘要： 讨论了Ⅰ-型三圈图和Ⅱ-型三圈图的正负惯性指数和零度问题. 主要通过删除悬挂的树和压缩内部路等方法,给出了两类特殊三圈图的正负惯性指数和零度的计算方法: Ⅰ-型三圈图的正负惯性指数(零度)等于一些树和一些双圈图(或单圈图或树)的正负惯性指数(零度)之和; Ⅱ-型三圈图的正负惯性指数(零度)等于一些树和一些简单三圈图的正负惯性指数(零度)之和, 对于点数较少的三圈图的正负惯性指数和零度利用软件Matlab计算得到.

关键词: 正惯性指数, 三圈图, 负惯性指数, 零度

Abstract: The problem how to calculate the positive and negative inertia indexes and nullity of Ⅰ-type and Ⅱ-type tricyclic graphs are discussed. By deleting pendant trees and compressing internal paths, a method of calculating the positive and negative inertia indexes and nullity of the two kinds of tricyclic graphs is given. It is proved that the positive and negative inertia indexes and nullity of Ⅰ-type tricyclic graphs equal to the sum of some trees and bicyclic graphs(or unicyclic graphs or trees), respectively; the positive and negative inertia indexes and nullity of Ⅱ-type tricyclic graphs equal to the sum of some trees and simple tricyclic graphs, and the positive and negative inertia indexes and nullity of simple tricyclic graphs can be calculated by Matlab.

Key words: negative inertia index, tricyclic graph, positive inertia index, nullity

中图分类号:

O157.5

杨陈, 马海成. 两类特殊三圈图的正负惯性指数和零度[J]. 山东大学学报（理学版）, 2015, 50(02): 32-37.

YANG Chen, MA Hai-cheng. Positive and negative inertia indexes and nullity of two special kinds of tricyclic graphs[J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2015, 50(02): 32-37.

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两类特殊三圈图的正负惯性指数和零度

Positive and negative inertia indexes and nullity of two special kinds of tricyclic graphs

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