Cycles and spanning trees (Q1179106)
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scientific article; zbMATH DE number 23936
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Cycles and spanning trees |
scientific article; zbMATH DE number 23936 |
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Cycles and spanning trees (English)
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26 June 1992
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Given a connected graph \(G\), it is shown that the number of labelled spanning trees of \(G\) is equal to the determinant of a cycle-cycle incidence matrix. Using this cycle-based approach, it is seen that the graph of a convex polyhedron and its dual have the same number of spanning trees. The method can also be used to show that certain sequences of algebraic numbers can be represented by a recursive formula using only integers.
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adjacency matrix
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incidence matrix
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cycles
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spanning trees
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algebraic numbers
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