JournalslemVol. 58, No. 1/2pp. 125–130

The surjectivity of the combinatorial Laplacian on infinite graphs

  • Tullio Ceccherini-Silberstein

    Università del Sannio, Benevento, Italy
  • Michel Coornaert

    Université de Strasbourg, France
  • Jozef Dodziuk

    The CUNY Graduate Center, New York, United States
The surjectivity of the combinatorial Laplacian on infinite graphs cover

Abstract

Given a connected locally finite simplicial graph GG with vertex set VV, the combinatorial Laplacian ΔG ⁣:RVRV\Delta_G \colon \mathbb R^V \to \mathbb R^V is defined on the space of all real-valued functions on VV. We prove that ΔG\Delta_G is surjective if GG 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, pp. 125–130

DOI 10.4171/LEM/58-1-5