The study of topological indices based on distance in a graph in biological sciences, physical - chemistry and QSAR and QSPR studies started from 1947 when Harold Wiener introduced the Wiener index to establishing the relationships between physico-chemistry properties of alkenes and the structures of their molecular graphs. Recent progresses in nano technology caused more attention in calculating topological indices of important molecular graphs such as nanotubes, nanocones and fullerenes. In this monograph, we present an algorithm for computing topological indices based on distance in a graph. By the algorithm the distance between all pairs of vertices is determined and then distance-based topological indices of a graph can be computed. The proposed algorithm is applied to computing the six topological indices: Wiener index, reverse Wiener index, edge Wiener index, eccentric connectivity index, Szeged index and Padmakar-Ivan index for some family of nano structures. Finally, some topological indices such as the Wiener index, the Szeged index, the edge Wiener index, eccentric connectivity index, additively harary index are investigated under some graph operations.