Connectivity and transportation description of graphs

The purpose of this article is to describe the design of mesh satellite systems that require no central controllers. We thereby construct the configuration of the system as the union of the graph that describes the client's demands, and another graph of small size, such that the resulting graph is strongly connected, and of out degrees and diameter that do not exceed the given requirements. Finally, we construct a routing table that provides the fastest way to distribute messages between every two clients in the system. Moreover, the suggested routing table simplifies the task of walking along the shortest paths. The novelty of the paper is that it brings graphs theory methods to solve problems in the design of mesh satellite systems in order to make them practical and increase their share in satellite communication.