Forest decompositions of graphs with cyclomatic number 2
Edward J. Farrell · International Journal of Mathematics and Mathematical Sciences · 1982
The simple tree polynomials of the basic graphs with cyclomatic number 3 are derived. From these results, explicit formulae for the number of decompositions of the graphs into forests with specified cardinalities are extracted. Explicit expressions are also given for the number of spanning forests and spanning trees in the graphs. These results complement the results given in [1].