ENUMERATION OF SPANNING TREES ON GENERALIZED PSEUDOFRACTAL NETWORKS

摘要

In this paper, we calculate the number of spanning trees on two families of generalized pseudofractal networks with two controllable parameters. The initial state is a complete graph with an arbitrary number of nodes as a generalization of a triangle. In the subsequent steps, each existing edge (newly produced edge) gives birth to finite new nodes. Using the electrically equivalent transformations, we obtain the changes of edge weights of corresponding equivalent networks and derive the relationships for enumerating spanning trees between original networks and transformed networks. Finally, we obtain closed-form formulas for the number of spanning trees, which is verified by numerical simulations.