Graph Reconstruction and Quantum Statistical Mechanics
  We study in how far it is possible to reconstruct a graph from various Banach algebras associated to its universal covering, and extensions thereof to quantum statistical mechanical systems. It turns out that most the boundary operator algebras reconstruct only topological information, but the statistical mechanical point of view allows for complete reconstruction of multigraphs with minimal degree three. 
Gunther Cornelissen and Matilde Marcolli
math.OA