Some Classes of 3-Gamma c-Critical Graph

Dominating set in a graph G is a connected dominating set of G if it induces a connected subgraph of G. The minimum number of vertices in a connected dominating set of G is called the connected domination number of G, and is denoted by gamma_c(G). The purpose of this paper is to initiate an investigation of those graphs which are critical in the following sense: for each v, u epsiv V(G) with v not adjacent to u, gamma_c(G + vu) < gamma_c(G). Thus, G is k- gamma_c- critical if gamma_c(G) = k and for each edge e not in E(G),gamma_c(G) < k. we give some classes of 3- gamma_c- critical graph.