il , , lsoperimetric Inequalities for Graphs , and Superconcentrators

il , , lsoperimetric Inequalities for Graphs , and Superconcentrators
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发表时间：
1985
期刊：
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影响因子：
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通讯作者：
N. Alon;V. Milman
N. Alon;V. Milman
中科院分区：
其他
文献类型：
--
作者：
N. Alon;V. Milman

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给出了图族渐近等周不等式的一般方法。其中一些不等式已被应用于泛函分析，这种方法使用与图相关的某个矩阵的第二小特征值，并且它是以前用于黎曼流形的方法的离散版本。也得到了一些结果的图的谱，显示这个特征值是如何相关的图的结构。结合这些结果与一些已知的结果群表示许多新的例子构造明确的线性尺寸的扩展和超集中。1985年，学术出版社。Inc.
A general method for obtaining asymptotic isoperimetric inequalities for families of graphs is developed. Some of these inequalities have been applied to functional analysis, This method uses the second smallest eigenvalue of a certain matrix associated with the graph and it is the discrete version of a method used before for Riemannian manifolds. Also some results are obtained on spectra of graphs that show how this eigenvalue is related to the structure of the graph. Combining these results with some known results on group representations many new examples are constructed explicitly of linear sized expanders and superconcentrators. ‘i:\ 1985 Academic Press. Inc.