On domination critical graphs with cutvertices having connected domination number 3

A subset of vertices D of a graph G is a dominating set for G if every vertex of G not in D is adjacent to one in D. A dominating set for G is a connected dominating set if it induces a connected subgraph of G. The connected domination number of G, denoted by γc(G), is the minimum cardinality of a connected dominating set. Graph G is said to be k−γc−critical if γc(G) = k but γc(G+e) < k for each edge e / ∈ E(G). In this paper, we investigate the structure of connected domination critical graphs with cutvertices. We also establish a characterization of 3 − γc−critical graphs with cutvertices.