Abstract
Applying a well-known theorem due to Eidelheit, we give a short proof of the surjectivity of the combinatorial Laplacian on a connected locally finite undirected simplicial graph G with countably infinite vertex set V established in [1]. In fact, we show that every linear operator on \(\mathbb {K}^V\) which has finite hopping range and satisfies the pointwise maximum principle is surjective.
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Kalmes, T. A short remark on the surjectivity of the combinatorial Laplacian on infinite graphs. RACSAM 110, 695–698 (2016). https://doi.org/10.1007/s13398-015-0258-y
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Keywords
- Combinatorial Laplacian
- Eidelheit’s Theorem
- Surjectivity
Mathematics Subject Classification
- 46A04
- 05C63