Construction and estimation of dominating sets in communication structures

The solution to determine and estimate domination numbers for several class of graphs of diameter 2, and suggest methods for constructing such graphs, including those with minimum no of edges was obtained. The problem of constructing and estimating dominating sets in graph with fixed diameter arises, as all the elements are available to each other to a certain extent, and a given number of central nodes directly communicating with all other elements is present. The estimation of the domination number for graph of diameter 2 is done by computing the constraints on the degrees of vertices. In this case the presence of Hamiltonian chain in the graph Gε ω makes it possible to sharpen the inequalities. The result obtained, makes it possible to design communication networks for the case that gives availability characteristics.