On graphs whose smallest eigenvalue is at least \(-1-\sqrt 2\) (Q1899436)
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scientific article; zbMATH DE number 803762
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On graphs whose smallest eigenvalue is at least \(-1-\sqrt 2\) |
scientific article; zbMATH DE number 803762 |
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On graphs whose smallest eigenvalue is at least \(-1-\sqrt 2\) (English)
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26 October 1995
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This paper shows that if the smallest eigenvalue of a graph \(H\) exceeds a fixed number larger than the smallest root \((\approx- 2.4812)\) of the polynomial \(x^3+ 2x^2- 2x- 2\), and if every vertex of \(H\) has sufficiently large valency, then the smallest eigenvalue of \(H\) is at least \(-1-\sqrt 2\) and the structure of \(H\) is completely characterized through a new generalization of line graphs.
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smallest eigenvalue
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line graphs
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