Abstract
Subdivision is an important aspect in graph theory which allows one to calculate properties of some complicated graphs in terms of some easier graphs. Recently, the notion of r-subdivision was similarly defined as a quite useful generalization by adding r new vertices to each edge. Also the double graphs are used to ease some calculations, especially with the chemical graphs. Topological graph indices have become popular due to their applications in chemistry or related areas due to their advantages over time and money consuming laboratory experiments. In this paper, we calculate one of the topological graph indices, namely the Narumi-Katayama index of the subdivision, r-subdivision, double, subdivision of double and double of subdivision graphs of any given graph. We give some symmetry relations and results for the well-known graph classes.