International Journal of Mathematics and Mathematical Sciences
Volume 6 (1983), Issue 3, Pages 535-543

Forest decompositions of graphs with cyclomatic number 3

E. J. Farrell

Department of Mathematics, The University of the West Indies, St. Augustine, Trinidad and Tobago

Received 15 June 1982

Copyright © 1983 E. J. Farrell. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


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].