Leonhard Paul Euler's Graph Theory

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1.1 Introduction Leonhard Paul Euler (1707-1783), a pioneering Swiss mathematician, who spent most of his life in Russia and Germany. Euler solved the first problem using graph theory and thereby led the foundation of very vast and important field of graph theory. He created first graph to simulate a real time place and situation to solve a problem which was then considered one of the toughest problems. That is, he solved the ‘Konigsberg bridge’ problem using graph theory and so the history of graph theory can be traced to 1736. The ‘Konigsberg bridge’ problem originated in the city of Konigsberg, Prussia lies along the Pregel River. The river was divided the city of Konigsberg into four regions which are two large islands (A and D) and two opposite banks (B and C). These islands and banks were connected by seven bridges as shown in Figure 1.1. Seven bridges were built hence the people of the city could get from one part to another. However, the villagers’ staying there wondered whether it was possible to have a walk which passes through all the bridges once and only once and return to the starting point. But, it is showing unexpected result that no one could find such a walk because there is no Eulerian circuit. Because of the villagers discussed whether it was possible to walk over every bridge in the town without using any bridge twice, so the problem had caught the attention of Euler. In 1736, Euler came out with the solution in terms of graph theory. He solved the

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