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Forest decompositions of graphs with cyclomatic number 3. (English) Zbl 0535.05023
A graph G has cyclomatic number n if n is the fewest number of edges whose removal will result in an acyclic graph. Simple tree polynomials of the basic graphs with cyclomatic number 3 are derived. These results are used to develop formulae for the number of spanning trees with specified cardinalities. Expressions are also given for the number of spanning forests and spanning trees in graphs of cyclomatic number 3.
Reviewer: J.Mitchem
MSC:
05C05 Trees
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