@MISC{n.n._graphs,basic, author = {n.n.}, title = { Graphs, Basic Notions }, year = {} }

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Abstract

Graphs are mathematical structures that have many applications to computer science, electrical engineering and more widely to engineering as a whole, but also to sciences such as biology, linguistics, and sociology, among others. For example, relations among objects can usually be encoded by graphs. Whenever a system has a notion of state and state transition function, graph methods may be applicable. Certain problems are naturally modeled by undirected graphs whereas others require directed graphs. Let us give a concrete example. Suppose a city decides to create a public-transportation system. It would be desirable if this system allowed transportation between certain locations considered important. Now, if this system consists of buses, the traffic will probably get worse so the city engineers decide that the traffic will be improved by making certain streets one-way streets. The problem then is, given a map of the city consisting of the important locations and of the two-way streets linking them, find an orientation of the streets so that it is still possible to travel between any two locations. The problem requires finding a directed graph, given an undirected graph. Figure 5.1 shows the undirected graph corresponding to the city map and Figure 5.2 shows a proposed choice of one-way streets. Did the engineers do a good job or are there locations