Enumerating spanning trees of vertex-edge-growth graph

Abstract

Abstract The problem of determining the number of spanning trees of graph having interesting structural properties such as the scale-free feature is attractive in science community. In this paper, we first present a class of outer-planar and self-similar graphs N(t) by using vertex-edge-growth operation. According to specific topological structure, we calculate the average degree, and show that the model N(t) is sparse. Then, we develop a series of iterative methods in order to obtain an exact solution of the total number of spanning trees of the model N(t), and also illustrate the corresponding spanning tree entropy. The calculation method used can be suitable for enumerating spanning trees of other graphs with similar properties.