Given a connected locally finite simplicial graph with vertex set , the combinatorial Laplacian is defined on the space of all real-valued functions on . We prove that is surjective if is infinite.
Cite this article
Tullio Ceccherini-Silberstein, Michel Coornaert, Jozef Dodziuk, The surjectivity of the combinatorial Laplacian on infinite graphs. Enseign. Math. 58 (2012), no. 1/2, pp. 125–130DOI 10.4171/LEM/58-1-5