A subset S of nodes in a graph G is k-connected m-dominating set ((k , m)-cds) if the subgraph G[S] induced by and every $$v \in V {\setminus } S$$ has at least m neighbors S. In k -Connected -Dominating Set m)-CDS) problem, goal to find minimum weight (k, m)-cds node-weighted graph. For $$m \ge k$$ we obtain following approximation ratios. unit disk graphs improve ratio $$O(k \ln k)$$ Nutov (I...

The new type of paranormal operators that have been defined in this study on the Hilbert space, is operators. In paper we introduce and discuss some properties concept such as: sum product two paranormal, power paranormal. Further, relationships between other kinds studied.