Generation of Trees without Duplications

Recent emphasis on the use of electronic digital computers has focused attention on a number of practical problems which were hitherto treated on an "existence" basis. One problem which arises in computer analysis of electrical networks is the listing of all trees in the network. Any practically useful scheme must find all the trees of the network without generating duplicates (for practical networks the number of trees exceeds the fast memory of any computer and, hence, slows down search for duplicates). Also, the trees must be generated by replacement of one branch at a time in order to keep track of signs (for active network analysis). A practical procedure satisfying these conditions is presented in this paper.