Counting spanning trees of a type of generalized Farey graphs

The Farey graph Fn is derived from the famous Farey sequence and it is a small-world network with a connectivity distribution decaying exponentially. By using the Matrix-Tree theorem, Zhang et al. (2012) obtained the exact formula of the number of spanning trees of Fn. In this paper, by using the electrical network method, we consider a type of generalized Farey graphs and give the exact solution for the number of spanning trees of these generalized Farey graphs, which generalizes some previous results about the Farey graphs. •We define a type of generalized Farey graphs.•We consider the number of spanning trees of a type of generalized Farey graphs.•We obtain the closed enumerative formula of the number of spanning trees of a type of generalized Farey graphs.