Connected domination critical graphs with a block having maximum number of cut vertices

摘要

A set D of vertices in a graph G is a dominating set if every vertex in V(G)−D is adjacent to a vertex in D. If the subgraph induced by the set D is connected, then D is a connected dominating set in G. The connected domination number of G, γc(G), is the minimum cardinality of a connected dominating set of G. A graph G is k-γc-critical if γc(G)=k and γc(G+uv)