A definition concerning the spanning sub graph and spanning sub graph circle is given. Use the enumerating methods of spanning sub circle; seek out the spanning sub graph of spanning trees. The theorems of constructing and enumerating the spanning trees are proved. The methods of enumerating and constructing connected graph spanning tree are proposed. The application examples of construction theorem and enumerating theorem are given the spanning sub graph's number of five plane graph and the construction of Constituent sub-graph are introduced, thus verifying constructing and enumerating theorem are useful and effective. This method Is a Simple and easy method to construct the spanning tree of connected graph.
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