| 图的Nordhaus Gaddumm型的代数连通度的界 |
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| 引用本文： | 吕大梅,杜娟,吕嘉钧.图的Nordhaus Gaddumm型的代数连通度的界[J].浙江大学学报(理学版),2009,36(6):616-619. |
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| 作者姓名： | 吕大梅 杜娟 吕嘉钧 |
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| 作者单位： | 南通大学,理学院,数学系,江苏,南通,210007 |
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| 基金项目： | Supported by NSFC （10671033） . The Natural Science Foundation of Nantong University （08Z003）. |
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| 摘 要： | 设图G是n阶的单图，G＇是它的补图．用a（G）表示图G的代数连通度．在很多文献中，已经研究了邻接谱半径的Nordhaus—Gaddum型的界的问题．本文进一步探讨了代数连通度的Nordhaus—Gaddum型的界．得到：对树和其他一些图，a（G）＋a（G＇）≥1成立，并刻画了等式成立时的图的特征．根据这些结果，最后提出这样一个猜想：对n阶的单图G，有n（G）＋n（G＇）≥1.
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| 关 键 词： | N—G型 代数连通度 界 |
A sharp lower bound for the algebraic connectivity of the Nordhaus-Gaddumm type |
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| L Da-mei,DU Juan,L Jia-jun.A sharp lower bound for the algebraic connectivity of the Nordhaus-Gaddumm type[J].Journal of Zhejiang University(Sciences Edition),2009,36(6):616-619. |
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| Authors: | L Da-mei DU Juan L Jia-jun |
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| Institution: | L(U) Da-mei,DU Juan,L(U) Jia-jun |
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| Abstract: | Let G be a simple graph with n vertices and Gc be its complement graph.Let a(G) be the algebraic connectivity of G.The bound for the spectrum of the Nordhaus-Gaddum type has been studied in many papers while this paper,the bound for the algebraic connectivity of the Nordhaus-Gaddum type is observed.For the trees and some other graphs,a(G) + a(Gc)≥1 is obtained and the graphs which achieve the bound is also characterized.As a result,the following conjecture is given: Let G be a graph of order n,then a(G)+a(Gc)≥1. |
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| Keywords: | Nordhaus-Gaddum type algebraic connectivity bound |
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