Abstract
It is revealed from the previous studies that there is a strong relation between the chemical characteristic of a chemical compound and its molecular structure. Topological indices defined on the molecular structure of biomolecules can help to gain a better understanding of their physical features and biological activities. Eccentricity connectivity indices are distance-based molecular structure descriptors that have been used for the mathematical modeling of biological activities of diverse nature. As the porphyrin has photofunctional properties, such as a large absorption cross-section, fluorescence emission, and photosensitizing properties, due to these properties, porphyrin dendrimers can be used as photofunctional nanodevices. In this paper, we compute the exact formulae of different versions of eccentric connectivity index and their corresponding polynomials for a class of porphyrin-cored dendrimers. The results obtained can be used in computer-aided molecular design methods applied to pharmaceutical engineering.
Highlights
In this era of rapid technological development, a large number of new nanomaterials, crystalline materials, and drugs emerge every year
A hydrogen-depleted molecular graph is the molecular graph with hydrogen vertices deleted
By molecular structure analysis, eccentricity calculating and mathematical derivation, we have computed the precise values of different versions of eccentric connectivity indices and their corresponding polynomials for a class of porphyrin-cored dendrimers
Summary
In this era of rapid technological development, a large number of new nanomaterials, crystalline materials, and drugs emerge every year. Numerous kinds of experiments have proven that these polymers with well-defined structures and topological architectures exhibited an array of applications in medicine [10] In these times, dendrimers are inviting the interest of a great number of researchers because of their remarkable physical and chemical properties and the wide range of promising applications in different fields [11,12,13]. We have been attracted to studying the mathematical properties of the eccentricity based topological indices and their polynomial versions of a class of dendrimers. Initiated the study of another distance-based topological index, termed as the eccentric connectivity index, of the graph G, described as. We will study the different topological indices and polynomials of the molecular graph of porphyrin-cored 2, 2-bis (methylol) propionic acid dendrimers. The synthesis and characterization of this dendrimer are described by Vestberg et al (see [35])
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