Path decompositions of chains and circuits (Q793050)
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scientific article; zbMATH DE number 3855152
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Path decompositions of chains and circuits |
scientific article; zbMATH DE number 3855152 |
Statements
Path decompositions of chains and circuits (English)
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1983
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For each spanning subgraph C of G consisting of paths \(P_ 1,P_ 2,...,P_ k\) let f(i) be the number of vertices in \(P_ i\), and let \(w(C)=\prod^{k}_{i=1}w_{f(i)}\) where \(w_ 1,w_ 2,w_ 3,...\) are indeterminates. The path polynomial of G is \(\sum w(C)\) where the summation is taken over all of the path covers of G. The path polynomials of paths and cycles are derived.
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path decomposition
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path polynomial
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