Spanning tree enumeration by bipartite subgraph separation

Enumerating functions which, compared with existing techniques, greatly facilitate counting the spanning trees of certain classes of graphs are presented, with examples of their application. One of these functions gives the spanning tree count in terms of the spanning forests of the subgraph which results on separating, from the original ordinary graph , the complete bipartite subgraph defined by the incidence set of any one of its vertices. Another is the function derived by removing two disjoint incidence sets of a certain type from the graph.