A Systematic Approach to the Evaluation of Flowgraph Transmission Equations

Abstract

The paper describes an approach for the evaluation of flowgraph transmission equations in a routine and systematic manner. Starting with the mere listing of the edges of a flowgraph in a matrix, on the basis of vertex designation, a procedure is outlined for generating successively, all paths and loops in a flowgraph. Since all paths and loops are identified in terms of their associated vertices, the vertex-loop, path-vertex, and path-loop matrices are set up with considerable facility. An elementary set-theoretic approach is then developed for generating all sets of non-touching loops, enabling the determinant of the graph to be obtained in a simple and straightforward manner. From a consideration of the determinant of the graph so obtained and the path-loop matrix, the path co-factors are readily obtained.

A four-vertex flowgraph is considered for illustration.