Simple finite connected graphs G=V,E of p≥2 vertices are considered in this paper. A connected detour set of G is defined as a subset S?V such that the induced subgraph GS is connected and every vertex of G lies on a u?v detour for some u,v∈S. The connected detour number cdnG of a graph G is the minimum order of the connected detour sets of G. In this paper, we determined cdnG for three special classes of graphs G, namely, unicyclic graphs, bicyclic graphs, and cog-graphs for Cp, Kp, and Km,n.
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