In chemical graph theory, numerical parameters which characterizes the molecular topology and structure of a graph are de ned as topological indices. In QSAR/QSPR di erent theoretical properties of chemical compounds as well as molecular topological in- dices such as eccentric connectivity index (ECI ), modi ed eccentric connectivity (MECI), total eccentricity (TE), connective eccentricity index (CEI ), Zagreb indices, counting polynomials and many more are used to predict the bioactivity of chemical compounds. The purpose of this thesis is to compute the characteristics of distance based topological indices in certain graphs which also covers computation of distance based topological in- dices for some type of nanostructure such as dendrimers, nanocones, few networks and counting polynomials of Benzene structure which is embedded in periodic type surface.