# The surjectivity of the combinatorial Laplacian on infinite graphs

Authors
Type
Published Article
Publication Date
Mar 25, 2011
Submission Date
Mar 25, 2011
Source
arXiv
Given a connected locally finite simplicial graph $G$ with vertex set $V$, the combinatorial Laplacian $\Delta_G \colon \R^V \to \R^V$ is defined on the space of all real-valued functions on $V$. We prove that $\Delta_G$ is surjective if $G$ is infinite.