The degree distance seems to have been considered first in connection with certain chemical applications by Dobrynin and Kochetova (1994) and at the same time by Gutman (1994), who named it the Schultz index. For chemists, the use of computing tools became an obligation in order to manipulate molecular information that were, during the last years, numerically stocked on computers in databases with huge quantities. Mathematical chemistry is a branch of theoretical chemistry for discussion and prediction of the molecular structure using mathematical methods without necessarily referring to quantum mechanics. Chemical graph theory is a branch of mathematical chemistry which applies graph theory to mathematical modeling of chemical phenomena. Topological indices and graph invariants based on the distances between the vertices of a graph are widely used in theoretical chemistry for establishing relations between the structure and the properties of molecules.