Graph theory, as modern and young branches of mathematics, studies graphs which are abstract mathematical objects. The use of graph models for description or data structures is very common. Investigation of algorithms to solve problems using graph, is a very important part of computer science. The genetic algorithms represent a family of algorithms using some of genetic principles being present in nature, in order to solve particular computational problems. These natural principles are: inheritance, crossover, mutation, survival of the fittest, migrations and so on. The problems degree-limited graph of nodes considering the weight of the vertex or weight of the edges, with the aim to find the optimal weighted graph in terms of certain restrictions on the degree of the vertices in the subgraph. This class of combinatorial problems was extensively studied because of the implementation and application in network design, connection of networks and routing algorithms. It is likely that solution of MDBCS problem will find its place and application in these areas.
