Labeling and Comparison of Isomeric Tree-Like Polyphenyl Systems

Tree-like polyphenyl systems form an important class of compounds in chemistry, in particular material science and polymers. The importance can be seen in LEDs, transmitters, and electronics. In recent years, many extremal results regarding such systems under specific constraints have been reported. More specifically are the sub-categories of such systems with extremal Wiener indices. In this article, we provide a labelling of the vertices on each hexagon (i.e., the corresponding benzene ring), which facilitates the illustration of a treelike polyphenyl system with its corresponding tree structure. This approach helps to characterize the extremal tree-like polyphenyl systems with respect to the Wiener index and compare such systems in general within isometric molecules and between molecules of different underlying tree structures. The results can be used to order these systems, which will aid in predicting the physical properties of compounds. We also briefly examined tree-like polyphenyl systems that resulted from different tree structures.