Some results on the independence number of connected domination critical graphs

A --critical graph is a graph with connected domination number and for any pair of non-adjacent vertices and of . Let and be respectively the clique number and the independence number of a graph. In this paper, we prove that every --critical graph satisfies for . We also characterize all --critical graphs achieving the upper bound. For , we show that there are infinitely many --critical graphs satisfying . Thus, we conclude this paper with an open problem that every --critical graph for satisfies .