On Evaluation of the Graph Trees and the Driving Point Admittance

The evaluation of characteristic numbers for trees has been done either by drawing the graph trees or by setting up a "primitive node-pair connection matrix." In this paper a new algorithm called the foldant is proposed. This is an algebraic method equivalent to the drawing of the graph trees. When a node, say node
n
, is superposed upon another node, say node 1, any branch
ni
, where
i
is any third node, is now parallel to the branch
li
. This geometrical transformation can be described by the algorithm of the foldant. As a direct application, Maxwell's rule of the driving point admittance which is described in the Appendix of his classic book. can be rewritten in terms of the foldant. Thus, as far as the computation of driving point admittance is concerned, it is no longer necessary to write down a set of node or loop equations nor to remember the lengthy statement of Maxwell's original rule. In this paper, pertinent theorems are given, together with proofs. Examples are given to clarify the method of computation.