Mathematical Modeling using Graph Theory to study Electrical Circuits and Networks

Abstract

The main purpose of this thesis is to see as to how mathematician can understand electrical/ newlineelectronic circuits and as to how engineers can understand graph theory. This mutual benefit newlineis facilitated through translation of electrical circuits to graphs and graphs to electrical newlinecircuits. This mutual translation helps both graph theory and electrical engineering in the newlinesense that graph theory can incorporate some important electrical concepts so that a newlinecomplicated circuit can be conviently and easily analyzed by studying its graph. Similarly newlinebasic concepts in graph, theorems on graphs can be understood clearly by studying the newlinecorresponding electrical networks. It is possible to formulate new theorems/concepts on newlinegraph theory by looking at the corresponding circuits and conversely. We have shown how newlineconfiguration helps us to symbolize electrical components. newlineWe stress here that we have presented chapters 1, 2, 3 and 4 in our own way although some newlineof the ideas are not our original work. In the literature a concept called Hyper Graph is newlineintroduced but it is not of much use in applications. We have modified this concept to define newlinea new concept Multi-vertexed-edge which finds applications in representing transistors. newlineThe main difference between these two is brought out. We have demonstrated how electrical newlinecomponents can be symbolized using the concept of Configuration . Perhaps for the first newlinetime we have applied pure geometrical concepts of configurations to symbolize electronic newlinecomponents and build circuits. We have also demonstrated how Ohm s law and Kirchhoff s newlinelaws becomes so elegant and easy to understand by translation of these to graph theory. For newlinethis purpose we have introduced new concepts called Series and Parallel graphs along newlinewith weight of a graph . newlineWe have also demonstrated as to how Capacitated networks flow graphs find their natural newlineapplication to circuit theory. newline