Mathematical apparatus for finding the optimal configuration secure communication network with a specified number of subscribers

Information flows in the world are growing very quickly. The exchange of information is growing rapidly. In connection with this fact, the existing mathematical apparatus and its practical application are constantly developing. The scientific and mathematical apparatus is aimed at finding the optimal configuration of the information communication network, solving the problem of building protected channels for the transmission of a large amount of data. A scientific task arises to develop a new and improve the existing mathematical apparatus for finding the optimal configuration of a protected communication network with a given number of subscribers. This scientific work is dedicated to the solution of this urgent task. The paper formulated and proved four Lemmas. The formulation of the Lemma made it possible to prove two new theorems that allow solving the task of finding the optimal configuration of a protected communication network with a given number of subscribers. Solutions to both partial and general tasks of the process of optimization and protection of transmission channels of a large amount of data are provided. Thus, the paper proposes a solution to the scientific task of finding the optimal configuration of a protected communication network with a given number of subscribers. The direction of further research may be the development of a software implementation of the given mathematical apparatus.