International Journal of Mathematics and Mathematical Sciences
Volume 6 (1983), Issue 1, Pages 125-136

Forest decompositions of graphs with cyclomatic number 2

E. J. Farrell

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 [1] 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.