Abstract
This paper presents some important properties emanating from the pair of conjugate trees. The properties are obtained by resorting to the fundamental loops and cutsets in the circuit topology. The existence of such a pair is one of the conditions for a nonlinear resistive circuit to have one and only one DC solution.
Highlights
Graph Theory is used for the study of real-world Systems possessing a binary relation between elements of a certain set within the system description
This paper presents some important properties emanating from the pair of conjugate trees
A line of research developed in recent years has attempted to determine the relationships between the topology of a circuit and its functionality, which has derived in a deeper knowledge in the general problem of nonlinear circuits [3,4]
Summary
Graph Theory is used for the study of real-world Systems possessing a binary relation between elements of a certain set within the system description. Among other discipline (Circuit Theory) has received outstanding contributions from the study of graphs. Some of the contributions may be found in the solution to specific problems related to electrical network analysis, nonlinear circuit theory, circuit diagnosis and circuit synthesis [1,2]. One important work has been reported in [5] and [6], where a topological criterion for the existence and uniqueness of the solution of linear circuits has been proposed. This criterion is based on two definitions of Graph Theory: the pair of conjugate trees and the uniform partial orientation of the resistors. The attention is focused on several properties of the pair of conjugate trees; these are highlighted by looking at the resulting loop and cutset matrices
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