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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 G[S] is connected and every vertex of G lies on a u − v detour for some u, v ∈ S. 'e connected detour number cdn(G) of a graph G is the minimum order of the connected detour sets of G. In this paper, we determined cdn(G) for three special classes of graphs G, namely, unicyclic graphs, bicyclic graphs, and cog-graphs for Cp, Kp, and Km,n.

The Connected Detour Numbers of Special Classes of Connected Graphs