A measurement of the molecular topology of graphs is known as a topological index, and several physical and chemical properties such as heat formation, boiling point, vaporization, enthalpy, and entropy are used to characterize them. Graph theory is useful in evaluating the relationship between various topological indices of some graphs derived by applying certain graph operations. Graph operations play an important role in many applications of graph theory because many big graphs can be obtained from small graphs. Here, we discuss two graph operations, i.e., double graph and strong double graph. In this article, we will compute the topological indices such as geometric arithmetic index GA, atom bond connectivity index ABC, forgotten index F, inverse sum indeg index ISI, general inverse sum indeg index ISIα,β, first multiplicative-Zagreb index PM1 and second multiplicative-Zagreb index PM2, fifth geometric arithmetic index GA5, fourth atom bond connectivity index ABC4 of double graph, and strong double graph of Dutch Windmill graph D3p.