Test for Planarity of a Circuit Given by an Expression

In this paper a relationship among distinct Pn+1, cycles, distinct stable maximum transient feedback shift registers of order n+1, and stable feedback shift registers of order n will be presented. In the course of the discussion, two algorithms will be introduced. The first will provide a one-to-one mapping between distinct stable feedback shift registers of order n and distinct stable maximum-transient feedback shift registers of order n+1. The second will provide a one-to-one mapping between distinct maximum transient feed-back shift registers of order n+1 and distinct Pn+1, cycles. As a corollary to these relationships, an enumeration of the stable feed-back shift registers is obtained.