Erratum: "The problem of deficiency indices for discrete Schr\"odinger   operators on locally finite graphs"
  In this note we answer negatively to our conjecture concerning the deficiency indices. More precisely, given any non-negative integer $n$, there is locally finite graph on which the adjacency matrix has deficiency indices $(n,n)$. 
Sylvain Golenia, Christoph Schumacher
math.SP math-ph math.FA math.MP