Euler's idoneal numbers and an inequality concerning minimal graphs with a prescribed number of spanning trees. (Q2856915)
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scientific article; zbMATH DE number 6221243
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Euler's idoneal numbers and an inequality concerning minimal graphs with a prescribed number of spanning trees. |
scientific article; zbMATH DE number 6221243 |
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30 October 2013
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spanning tree
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math.CO
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Euler's idoneal numbers and an inequality concerning minimal graphs with a prescribed number of spanning trees. (English)
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The authors consider the following problem: what is the smallest graphs (either in terms of the number of vertices, or of the number of edges), which contains exactly a given number of spanning trees. This problem was first considered in [\textit{J. Sedláček}, Can. Math. Bull. 13, 515--517 (1970; Zbl 0202.23501)]. Here, some new bounds on problem are obtained. The central part of the paper comes from explicitly constructed graphs whose number of spanning trees can be controlled.
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