Abstract
A characteristic graph is a tree representative of its corresponding benzenoid (cyclic) graph. It may contain necessary information of several properties of benzenoids. The PI-index of benzenoids and their characteristic graphs are compared by correlating it to a structural property (π-electron energy) of the benzenoids using MLR analysis. PI index being applicable to both trees and cyclic graphs, yielded required results for benzenoid and their characteristic graph.
Highlights
Topological indices are a numerical representation of a chemical graph, which is obtained by imposing certain conditions on atoms, vertices, or both
First introduced by (Balaban et al 1976), it consists of vertices placed in the center of benzenoid rings, and edges connecting these vertices as shown in the figure 1
The question arises whether we can compare the PI indices of both of them? If yes, we can find all the information related to a cyclic graph using that of its tree’s. This is done by correlating any structural property of the given set of samples with PI index of their characteristic graphs and benzenoid graphs
Summary
Topological indices are a numerical representation of a chemical graph, which is obtained by imposing certain conditions on atoms, vertices, or both. The first application of these indices in the studies of structure-properties relationship (QSPR) was proposed by Weiner. For many years, more than one hundred topological indices were introduced which has enabled to characterize the physicochemical properties of most of the molecules. The most commonly used are Wiener-, Szeged -, PI, Balaban, Schultz’s and Sadhana index. A characteristic graph (or a dualistic graph) is a tree representative of the corresponding benzenoid (cyclic) graph (Benzenoid graphs are graph theoretical representations of benzenoid hydrocarbons). First introduced by (Balaban et al 1976), it consists of vertices placed in the center of benzenoid rings, and edges connecting these vertices as shown in the figure 1
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