Kato's inequality and Liouville theorems on locally finite graphs
  In this paper we study the Kato' inequality on locally finite graph. We also study the application of Kato inequality to Ginzburg-Landau equations on such graphs. Interesting properties of Schrodinger equation and a Liouville type theorem are also derived. 
Li Ma, Xiangyang Wang
math.AP math.CA math.DG math.DS