On Unistor Graphs

There are a number of applications of graph theory to the solutions of problems in electrical networks, switching circuits, and communication nets. These applications involve modeling a system by a graph and describing the properties of the system in terms of this corresponding graph. In this paper it is shown that a linear system can be modeled by a graph of unistors; that is, an oriented edge with flow proportional to the initial vertex. The solution of the system is then obtained by means of products of directed trees. There is no calculation of cofactors as an intermediate step, and no extra calculation to determine the sign of the solution. In order to achieve the result, the relationships between the directed trees forming a unistor graph and their associated incidence matrices are developed and techniques for calculating determinants and cofactors of linear systems by means of directed trees and directed 2-trees are given.