Generation of trees, cotrees and 2-trees of a linear graph

A new algorithm for finding all trees, cotrees and 2-trees in a connected linear graph is given. The procedure will not generate any duplication, redundancies or cancellation of terms. The method given is based only on the definition of tree, so that no complexity arises. Further, it is shown that, if a certain condition is satisfied by the graph, the 2-trees can be obtained directly from the trees that have been generated. An illustrative example on the algorithm is also given.