Phragmén–Lindelöf type results for a class of parabolic equations on infinite graphs

We discuss Phragmén–Lindelöf type theorems for parabolic equations with a variable density, posed on infinite weighted combinatorial graphs. In particular, we address the relation between the behaviour of the density and the uniqueness class. We also show that our conditions on the density are sharp. The results have been recently obtained jointly with S. Biagi and G. Meglioli.