A note on the domination equalities (Q1769322)

The article is aimed at establishing features of graphs, being tied to the number of vertices and to the connectivity. The paper consists of two parts: the first one contains most of definitions and symbols used, whereas the second part includes the basic results reflected by several theorems, prepositions and corollaries. These results say that the equality of the independent domination number and the independence number of a graph is bounded by \(n/2\), where \(n\) is the number of vertices of the graph. It is also proved that such a graph has a complete bipartite subgraph.