A Radio Mean D-distance labeling of a connected graph G is an injective map f from the vertex set V(G) to ℕ such that for two distinct vertices u and v of G, d D (u, v) + + () 2 ≥ 1 + diam D (G), where d D (u, v) denotes the D-distance between u and v and diam D (G) denotes the D-diameter of G. The radio mean Ddistance number of f, rmn D (f) is the maximum label assigned to any vertex of G. The radio mean D-distance number of G, rmn D (G) is the minimum value of rmn D (f) taken over all radio mean D-distance labeling f of G. In this paper we find the radio mean D-distance number of graph obtained from graph operation.

with respect to c is the k-tuple c(v) = (a 1 , a 2 ,. .. , a k) where a i is the number of edges incident with v that are colored i (1 ≤ i ≤ k). The k-labeling c is detectable if every two adjacent vertices of G have distinct codes. The minimum positive integer k for which G has a detectable k-labeling is the detection number det(G) of G. In this paper we obtain the detection number of some known graphs such as P n x P m , circular halin graph of level two, wheel, crown graph etc.