A proof of obtaining all the support trees of a connected graphwith the polynomials of its basic cutsets

There is inevitably some support trees in a connected graph. In general, there is not only one support tree in a graph. How to obtain all the support trees of a connected graph is an important problem in graph theory. It is a simple and feasible method to generate all the support trees of a graph by making use of the polynomial of its basic cutsets. But the existing theoretical proof to this method is overelaborate and tedious. In this paper, a simpler proof to the method is given to illustrate that it can be used to obtain all the different support trees of a connected graph.