The surjectivity of the combinatorial Laplacian on infinite graphs (Q353414)
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scientific article; zbMATH DE number 6187659
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | The surjectivity of the combinatorial Laplacian on infinite graphs |
scientific article; zbMATH DE number 6187659 |
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The surjectivity of the combinatorial Laplacian on infinite graphs (English)
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12 July 2013
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Summary: Given a connected locally finite simplicial graph \(G\) with vertex set \(V\), the combinatorial Laplacian \(\Delta_G\:\mathbb{R}^V\to\mathbb{R}^V\) is defined on the space of all real-valued functions on \(V\). We prove that \(\Delta_G\) is surjective if \(G\) is infinite.
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connected locally finite simplicial graph
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combinatorial Laplacian
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