| 正则图的代数连通度 |
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| 引用本文： | 周后卿,周琪. 正则图的代数连通度[J]. 四川师范大学学报(自然科学版), 2012, 0(2): 219-221 |
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| 作者姓名： | 周后卿 周琪 |
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| 作者单位： | 邵阳学院数学系;湖南农业大学经济学院 |
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| 基金项目： | 湖南省科技厅科技计划(2010JT4043)资助项目;邵阳市科技局科技计划项目(N1110)对 |
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| 摘 要： | 设G=(V,E)是一个具有n个顶点的简单图,A(G)是G的邻接矩阵,D(G)表示G的度对角矩阵,图G的拉普拉斯矩阵定义为L(G)=D(G)-A(G).若矩阵L(G)的特征值为μ1≥μ2≥…≥μn-1≥μn=0,则称μn-1为G的代数连通度.研究了正则图的代数连通度,得到了下列结论:μn-1≤(nrln(n-l))/(6n-8-4r-nln(n-1))这里,r表示正则图的度.
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| 关 键 词： | 正则图 拉普拉斯矩阵 代数连通度 |
Algebraic Connectivity of Regular Graphs |
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| ZHOU Hou-qing,ZHOU Qi. Algebraic Connectivity of Regular Graphs[J]. Journal of Sichuan Normal University(Natural Science), 2012, 0(2): 219-221 |
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| Authors: | ZHOU Hou-qing ZHOU Qi |
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| Affiliation: | 1.Department of Mathematics,Shaoyang College,Shaoyang 422004,Hunan; 2.Economic College,Hunan Agricultural University,Changsha 410128,Hunan) |
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| Abstract: | Let G=(V,E) be a simple graph with vertex set V={v1,v2,…,vn} and edge set E.Let A(G) be the adjacency matrix of G and D(G) the diagonal matrix of vertex degrees.The Laplacian matrix of G is L(G)=D(G)-A(G).The eigenvalues of L(G) are denoted byμ1≥μ2≥ …≥μn-1≥μn=0.Then,μn-1 is called the algebraic connectivity of G.In this paper,we prove that μn-1≤(nrln(n-l))/(6n-8-4r-nln(n-1)). |
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| Keywords: | regular graph Laplacian matrix algebraic connectivity |
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