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Explorations in Topology by David Gay

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The reader is introduced to the Bridges of Königsberg problem made famous by the eighteenth-century Swiss mathematician, Leonhard Euler. The reader is led to understand that the problem has no solution. Through this, the reader is also introduced to the notion of a network (i.e., graph) consisting of edges and vertices and to the notion of finding a path starting at a vertex, traversing each edge once and only once, and returning to the starting vertex. Such a path is called an Euler circuit. The reader is led through the argument that if an Euler circuit exists for the network, then every vertex must be of even order, the order of a vertex being the number of edges attached to it. An end-of-chapter investigation asks: given a network, ...

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