A subset D of V(D ) is said to be a (G, D) set of G if it is both a dominating and a geodetic set of G. The minimum cardinality among all (G, D) sets of G is called the (G, D)-number of G and is denoted by (G ). In this paper, the (G, D)- number of Middle graph of Path, Cycle, Fan graph, Join of two Fan graphs and Total graph of Fan graph are Calculated.