Networks with Applications

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Addis Ababa University


This project is conserned with a network and its applications. The project begins with pre-concepts of graph theory and focuses on one of the the well known application of graph theory called networks. The project on its main body begins by defining terms like network, flow , net flow, cutsetc.and concentrate on the basic ideas to obtain an optimal flow in a given network. The concept of network is helps to solve prblems related with the movement of commodity (or materials) from one location to another. Forinstance, an oil company must move crude oil from the oil field to its refinery, and a long-distance telephone company must move messages from one city to another. Even though, there are a lot of applications of networks, but this project deals on two of them, it’s application on menger’s theorem and obtaining the cardinality of the maximum matching in any bipartite graph. Menger’s theorem is proved easily using network flow method, and normally it is very awkward to prove it without using network flow problem. In maximum bipartite matching, the network flow suggests that ||=v ( for a flow in a network and a maximum matching in a bipartite graph by transforming the bipartite graph into a network



Networks with Applications