A short remark on the surjectivity of the combinatorial Laplacian on infinite graphs

作者：Kalmes T^*

来源：Revista de la Real Academia de Ciencias Exactas Fisicas y Naturales Serie A-Matematicas, 2016, 110(2): 695-698.

DOI：10.1007/s13398-015-0258-y

• Combinatorial Laplacian
• Eidelheit's Theorem
• Surjectivity

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 which has finite hopping range and satisfies the pointwise maximum principle is surjective.

• 出版日期2016-9