The problem of deficiency indices adjacency matrices on locally finite graphs

Sylvain Golenia (1) , Christoph Schumacher (2)

1 IMB - Institut de Mathématiques de Bordeaux
2 Chemnitz University of Technology / Technische Universität Chemnitz

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 adjency matrix has deficiency indices $(n,n)$.

Mots clés: adjacency matrix; deficiency indices; locally finite graphs

Domaines: Théorie spectrale [math.SP]; Analyse fonctionnelle [math.FA]; Physique mathématique [math-ph]

Sylvain Golenia, Christoph Schumacher. The problem of deficiency indices adjacency matrices on locally finite graphs. 2012. ⟨hal-00717815v1⟩