On 1-\(Z_m\)-well-covered and strongly \(Z_m\)-well-covered graphs. (Q2715989)
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scientific article; zbMATH DE number 1600958
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On 1-\(Z_m\)-well-covered and strongly \(Z_m\)-well-covered graphs. |
scientific article; zbMATH DE number 1600958 |
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20 July 2005
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strongly well-covered graph
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maximal independent set
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chordal graph
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On 1-\(Z_m\)-well-covered and strongly \(Z_m\)-well-covered graphs. (English)
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A graph \(G\) is \(Z_m\)-well-covered if every two maximal independent sets in \(G\) have the same cardinality modulo \(m\). If, in addition, every vertex-deleted (resp. edge-deleted) subgraph of \(G\) is \(Z_m\)-well-covered, then \(G\) is 1-\(Z_m\)-well-covered (resp. strongly \(Z_m\)-well-covered).NEWLINENEWLINEThe author proves several results on the structure of graphs of the latter two types.
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