Strong connections between the chemical characteristics of chemical compounds, materials and drugs and their topological structures have been proved by lots of previous research. For instance, they get the connections in melting point and boiling point. The chemical indices from these molecular topological structures turn out to be favorable for chemists, material and medical scientists, when they try to get the relevant chemical reactivity, biological activity and physical features. As a result, the shortage of the experiments can be covered and made up, if the conduct the study of the topological indices on the molecular structures. Meanwhile, the study can also make contributions by providing the theoretical evidence in chemical, pharmaceutical and material engineering. On the basis of graph analysis and computation derivation, some degree and distance mixing indices of some classes of Harary graphs and coronene polycyclic aromatic hydrocarbons are determined in the paper. Therefore, the study lay a theoretical foundation for the material properties.
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