On the Outer Connected Geodetic Number of a Graph

For a connected graph G of order at least two, a connected outer connected geodetic set S of G is an outer connected geodetic set such that the subgraph induced by S is connected. The minimum cardinality of a connected outer connected geodetic set of G is the connected outer connected geodetic number of G and is denoted by cgco(G). We determine bounds for it and characterize graphs which realize these bounds. Some realization results on the connected outer connected geodetic number of a graph are studied.