International Journal of Mathematics and Mathematical Sciences
Volume 6 (1983), Issue 1, Pages 125-136
Forest decompositions of graphs with cyclomatic number 2
Department of Mathematics, The University of the West Indies, West Indies, St. Augustine, Trinidad and Tobago
Received 16 June 1981; Revised 28 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 tree polynomials  of the basic graphs with cyclomatic number 2 are
derived. From these polynomials, results about forest decompositions are deduced. Explicit formulae are given for the number of decompositions of the basic graphs into forest with specified finite cardinalities.