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Kalil, C., de Castro, M., Silva, D. and Cortez, C. (2021) Applying Graph Theory and Mathematical-Computational Modelling to Study a Neurophysiological Circuit. Open Journal of Modelling and Simulation, 9, 159-171.
https://doi.org/10.4236/ojmsi.2021.92011

has been cited by the following article:

• TITLE: Solving Electrical Circuits via Graph Theory

  AUTHORS: Jan Vrbik

  KEYWORDS: Kirchoff’s Laws, Connected Graph, Incidence Matrix, Spanning Tree, Fundamental Cycles

  JOURNAL NAME: Applied Mathematics, Vol.13 No.1, January 25, 2022

  ABSTRACT: Solving for currents of an electrical circuit with resistances and batteries has always been the ultimate test of proper understanding of Kirchoff’s rules. Yet, it is hardly ever emphasized that a systematic solution of more complex cases requires good understanding of the relevant part of Graph theory. Even though this is usually not covered by Physics’ curriculum, it may still be of interest to some teachers and their mathematically inclined students, who may want to learn details of the rigorous approach. The purpose of this article is to provide a concise derivation of a linear set of equations leading to a unique solution of the problem at hand. We also present a simple computer program which builds such a solution for circuits of any textbook size.