Harmonic graphs with small number of cycles (Q1874351)
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scientific article; zbMATH DE number 1915533
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Harmonic graphs with small number of cycles |
scientific article; zbMATH DE number 1915533 |
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Harmonic graphs with small number of cycles (English)
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25 May 2003
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A graph is harmonic if its degree vector is also its principal eigenvector. Trivially, all regular graphs are harmonic. All harmonic trees were determined by \textit{S. Grünewald} [Appl. Math. Lett. 15, 1001-1004 (2002)]. Here the authors show that for any \(c>1\) the number of connected harmonic graphs with cyclomatic number \(c\) is finite, and they determine all harmonic graphs with cyclomatic number up to 4 (but those with cyclomatic number 4 without proof).
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harmonic graphs
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spectrum of graph
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cyclomatic number
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unicyclic graphs
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bicyclic graphs
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tricyclic graphs
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tetracyclic graphs
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regular graphs
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