Counting maximal distance-independent sets in grid graphs (Q2857030)
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scientific article; zbMATH DE number 6221384
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Counting maximal distance-independent sets in grid graphs |
scientific article; zbMATH DE number 6221384 |
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Counting maximal distance-independent sets in grid graphs (English)
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31 October 2013
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independent set
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grid graph
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Fibonacci
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Padovan numbers
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transfer matrix method
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\(G_{p,q,r} = (V, E)\) is called 3-dimensional grid graph of size \(p \times q \times r\) (or \((p,q,r)\)-grid graph) with vertex set NEWLINE\[NEWLINEV = \{ (i,j,k) : 1 \leq i \leq p, 1 \leq j \leq q, 1 \leq k \leq n \}NEWLINE\]NEWLINE and edge set NEWLINE\[NEWLINEE = \{ (i,j,k), (i',j',k') : |i - i'| + |j - j'| + |k - k'| = 1 \},NEWLINE\]NEWLINE where \(p\), \(q\), \(r\) are natural numbers. Some properties of the \((p,q,r)\)-grid graphs are discussed. Matrix representations of them are shown.
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