ENUMERATION OF SPANNING TREES ON GENERALIZED PSEUDOFRACTAL NETWORKS

作者：Jinmei Xiao, Jingyuan Zhang, Weigang Sun · 发表于：Fractals · 年份：2015 · DOI：10.1142/s0218348x15500218 · 被引用次数：5 · 研究领域：Complex Network Analysis Techniques、Complex Systems and Time Series Analysis、Theoretical and Computational Physics

In this paper, we calculate the number of spanning trees on two families of generalized pseudo- fractal 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.