Graph from Still Bridges to Dynamics Systems




The Pregel River in Königsberg (today Kaliningrad) has two islands, and at that time there were seven bridges connecting these islands and the banks of the river.  The problem was to stroll across each bridge exactly once and return to the starting point. The people of Königsberg tried this by taking random walks but with no success.  Euler solved the Königsberg bridge problem in 1736 whereby he replaced each land area by a point and each bridge by a line joining two points.  He showed that the problem is insoluble, and it was the first recorded mention of graph theory.  The modelling process could have been experienced in Euler’s mind, whether he made explicit of it or not, when he tried to solve the problem of the Königsberg bridge. However, this book provides detailed discussion on how one can use graph to construct a mathematical model of a given dynamic system.  The first two chapters of the book lay all the necessary elements of the methodology. The next three chapters shift to background of the three distinct dynamical systems, namely, refining process of palm oil, EEG signal of epileptic patient and pressurized water reactor.  Detail graphical construction for the three dynamical systems are elaborated in Chapter 6, Chapter 7 and Chapter 8, respectively.  Chapter 9 is the final chapter that glimpses on a frontier of graph theory and its application.

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