International Journal of Mathematics and Mathematical Sciences 
Volume 6 (1983), Issue 1, Pages 125-136
doi:10.1155/S0161171283000113

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

Abstract

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.