On the spectrum, the growth, and the diameter of a graph (Q1305521)
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scientific article; zbMATH DE number 1346885
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On the spectrum, the growth, and the diameter of a graph |
scientific article; zbMATH DE number 1346885 |
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On the spectrum, the growth, and the diameter of a graph (English)
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9 February 2000
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A lower bound is given for the harmonic mean of the growth in a finite undirected graph \(\Gamma\) in terms of the eigenvalues of the Laplacian of \(\Gamma\). For a connected graph, this bound is tight if and only if the graph is distance-regular. Bounds on the diameter of a ``sphere-regular'' graph follow. Finally, a lower bound is given for the growth in an infinite undirected graph of bounded degree in terms of the spectrum of its Laplacian. \(\copyright\) Academic Press.
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harmonic mean of the growth
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eigenvalues
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Laplacian
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distance-regular
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diameter
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spectrum
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