| 有关连通图谱半径的一些可达下界 |
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| 引用本文： | 龚和林. 有关连通图谱半径的一些可达下界[J]. 华东师范大学学报(自然科学版), 2012, 2012(4): 18-26 |
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| 作者姓名： | 龚和林 |
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| 作者单位： | 上饶师范学院 数学与计算机科学学院,江西上饶,334001 |
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| 基金项目： | 江西省教育厅科技项目青年基金，国家特色专业，上饶师范学院课题 |
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| 摘 要： | 讨论连通简单图的谱半径的下界问题.证明了关于途径数的一个不等式,进而利用最大、最小度、平均度、2-度和k-途径数给出图的谱半径一些新的下界.再运用相似矩阵特性与Weyl不等式,并利用途径数得到图谱半径的另一下界.同时刻画了上述下界的全部极值图.
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| 关 键 词： | 邻接矩阵 谱半径 Perron特征向量 下界 |
| 收稿时间： | 2011-08-01 |
Some sharp lower bounds for spectral radius of connected graphs |
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| GONG He-lin. Some sharp lower bounds for spectral radius of connected graphs[J]. Journal of East China Normal University(Natural Science), 2012, 2012(4): 18-26 |
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| Authors: | GONG He-lin |
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| Affiliation: | School of Mathematics and Computer Science, Shangrao Normal University, Shangrao Jiangxi 334001, China |
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| Abstract: | This paper studied lower bounds on the spectral radius of connected simple graphs and proved an useful inequality for the number of walks. Furthermore, some new lower bounds on the spectral radius of graphs were provided in terms of the maximum and minimum degree, the average degree, the 2-degree and the number of $k$-walks(with $k$ vertexes). By applying the properties of similar matrices and the Weyl inequalities, another lower bound was obtained by means of the number of $k$-walks. Simultaneously, all extremal graphs which achieve above bounds were also characterized. |
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| Keywords: | adjacency matrix spectral radius Perron eigenvector lower bound |
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