Graphs with constant \(\mu\) and \(\overline{\mu}\) (Q1379987)
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scientific article; zbMATH DE number 1121504
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Graphs with constant \(\mu\) and \(\overline{\mu}\) |
scientific article; zbMATH DE number 1121504 |
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Graphs with constant \(\mu\) and \(\overline{\mu}\) (English)
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24 March 1998
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A graph has constants \(\mu\) and \(\overline\mu\) if any two nonadjacent vertices have \(\mu\) common neighbours and any two adjacent vertices are both nonadjacent to \(\overline\mu\) vertices. It is proved that a connected graph \(G\) has constants \(\mu\) and \(\overline\mu\) if and only if the Laplacian of \(G\) has two distinct nonzero eigenvalues. Some constructions of such graphs are given.
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Laplacian
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eigenvalues
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