| 图和线图的谱性质 |
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| 引用本文： | 陈晏.图和线图的谱性质[J].高校应用数学学报(英文版),2002,17(3):371-376. |
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| 作者姓名： | 陈晏 |
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| 作者单位： | Dept.ofMath.,ZhejiangEducationInstitute,Hangzhou310012,China |
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| 摘 要： | Let G be a simple connected graph with n vertices and m edges,Lo be the line graph of G and λ1(LG)≥λ2 (LG)≥...≥λm(LG) be the eigenvalues of the graph LG,.. In this paper, the range of eigenvalues of a line graph is considered. Some sharp upper bounds and sharp lower bounds of the eigenvalues of Lc. are obtained. In oarticular,it is oroved that-2cos(π/n)≤λn-1(LG)≤n-4 and λn(LG)=-2 if and only if G is bipartite.
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| 关 键 词： | 图 线图 谱 性质 |
| 收稿时间： | 28 December 2001 |
Properties of spectra of graphs and line graphs |
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| Chen Yan.Properties of spectra of graphs and line graphs[J].Applied Mathematics A Journal of Chinese Universities,2002,17(3):371-376. |
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| Authors: | Chen Yan |
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| Institution: | (1) Dept. of Math., Zhejiang Education Institute, 310012 Hangzhou, China |
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| Abstract: | Let G be a simple connected graph with n vertices and m edges, L
G
be the line graph of G and λ
1 (L
G
) ≥ λ
2 (L
G
) ≥ … ≥ λ
m
(L
G
) be the eigenvalues of the graph L
G
. In this paper, the range of eigenvalues of a line graph is considered. Some sharp upper bounds and sharp lower bounds of
the eigenvalues of L
G
are obtained. In particular, it is proved that and λ
n
(L
G
) =−2 if and only if G is bipartite. |
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| Keywords: | eigenvalue line graph Laplacian matrix |
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