Semi-Fredholmness of the Discrete Gauss-Bonnet Operator

Abstract

In the context of an infinite locally finite weighted graph, we give a necessary and sufficient
condition for semi-Fredholmness of the Gauss-Bonnet operator. This result is a discrete version of the theorem of Gilles Carron in the continuous case . In addition, using a criterion of Anghel, we give a sufficient condition to have an operator of Gauss-Bonnet with closed range. Finally, this work can be considered as an extension of the work of Colette Anné and Nabila Torki-Hamza.