Garbage Collection, Sunday Strolls, and Soldering Problems

Is there an area of mathematics that deals with garbage collection, Sunday strolls, and soldering problems all at once? Indeed there is, and it is called graph theory, a subject that considers the properties of configurations consisting of points and connecting lines such as the configuration shown in figure 2. (There is another meaning for the word graph, as in bar graph or graph of a function, which is not meant here.) The practical applications of graph theory are so widespread that this theory has become one of the most important and rapidly growing areas of applied mathematics in recent years. What is especially unique about it, however, is the extreme simplicity of the basic ideas. Because of this dual nature of practicality and simplicity, graphs have been creeping into the high school curriculum lately, often in the form of optional topics.