Graphs Carbon/Heteroatom

Figure 3. A specific structure and two forms of its reduced chemical graph based on carbon/heteroatom components.

The performance of the carbon/heteroatom reduced graph in the same search is slightly better for this database and these queries 51 queries each retrieve only the associated generic. In the worst cases, five queries retrieve only two additional generics. Figure 6 illustrates these results. 

Recently, the chemical graph theory was systematically developed to characterize and evaluate polyene molecular structures [52], i.e., those compounds which play a central role in battery application. Especially for carbon electrodes, the role of inserted heteroatoms such as nitrogen was systematically investigated by Ukrainian workers [53,54]. Such developments may adopt a high importance in future battery work. 

Moreover, the composite reference ETA index, denoted as tir, is calculated as the composite ETA index from a molecular graph where all heteroatoms are substituted by carbon atoms and all the multiple bonds by single bonds. Then, the functionality index Tip is defined as the difference between the composite reference ETA index and the composite ETA index ... 

The reduced graph may contain vertices representing the cyclic and acyclic portions of the molecule or contiguous groups of carbon or heteroatoms. 

A second and complementary basis for chemical graph reduction is provided by differentiation between contiguous assembUes of carbon atoms and heteroatoms. This is illustrated in Figure 3 for the same structure. Once again, it is possible to ring the changes on the detail given. 

RING/NON RING REDUCED GRAPH WITH CARBON AND HETEROATOM RANGES... 

---