On directed labelings of stars (Q2799883)
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scientific article; zbMATH DE number 6568627
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On directed labelings of stars |
scientific article; zbMATH DE number 6568627 |
Statements
13 April 2016
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labellings
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directed labellings
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digraphs
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0.85812765
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0.8562114
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0.8473965
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0.84465796
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0.84432924
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On directed labelings of stars (English)
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For any directed graph \(D=(V,A)\) and injective function \(l\) from \(V\) to \(\{1,2, \dots, n\}\), the weight of an arc \((x, y)\) is defined as \(l(y)/l(x)\). The sum of all weights of arcs in \(D\) is written as \(\mu_l(D)\). The directed integer norm of \(D\), denoted by \(\| D\|_N\), is defined as the minimum of \(\mu_l(D)\) over all labellings \(l\). The authors find a labelling to produce the directed integer norm for any directed star of size \(n\).
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