work. The method of modeling and the contents of our articles [SL1], [SL2], [RIS1], [PB3], and [PB4] will be explained below. 2. The Method of Modeling

In this research, graph theory is applied for two purposes. One is to express the routing of communication and the other is to express the condition of roads. In both case, we require a directed graph in which each graph edge is replaced by a directed graph edge. Then to be able to add a value to each route, a weighted graph in which each graph edge has an associated numerical value is adopted in this research as well. In a communication route graph, the weight of an edge represents the intensity of an electric wave, the condition of a battery, and the moving speed of each mobile terminal. In road graphs, the weight of an edge represents bend conditions of a road, distances between crossings, and conditional probabilities of advancing directions based on the road situation. Moreover, to be able to improve the efficiency of routing, each mobile terminal needs to have information about mobile terminals of the neighborhood which can communicate directly with it. For this reason, we also add neighborhood information to each vertex in the graph of communication routing. The neighborhood of a vertex v in a graph is the set of all the vertices adjacent to v. In the example of Fig. 1, when terminal � wants to communicate with terminal � outside the area in which it can communicate directly, it is necessary to look for a terminal which can relay the communication. A linear search algorithm tracing each edge going out from � is the simplest way to find such a terminal, but it has an inefficient calculation cost. As opposed to this it is more efficient to find routing paths by using the information of vertex neighborhoods. In this example, by merely taking the union operation of the neighborhood of � and �, it becomes immediately clear that � is a relay terminal between � and �