Generation of trees and cotrees of a graph by decomposition

Generation formulas from which the sets of trees and cotrees of a graph are expressed as the ring sums or the unions of the Cartesian products of the sets of subgraphs of the component graphs which are obtained from the original graph by decomposition are presented. If the subgraphs of the component graphs are given, the procedure will not generate any duplications, redundancies or cancellations of terms. Methods of generating certain types of desired subgraphs of the component graphs, and illustrative examples, are also given.