Topological characterization of dendrimer, benzenoid, and nanocone.

Dendrimers are large and complex molecules with very well defined chemical structures. More importantly, dendrimers are highly branched organic macromolecules with successive layers or generations of branch units surrounding a central core. Topological indices are numbers associated with molecular graphs for the purpose of allowing quantitative structure-activity relationships. These topological indices correlate certain physico-chemical properties such as the boiling point, stability, strain energy, and others, of chemical compounds. In this article, we determine hyper-Zagreb index, first multiple Zagreb index, second multiple Zagreb index, and Zagreb polynomials for hetrofunctional dendrimers, triangular benzenoids, and nanocones.

Physical Analysis of Heat for Formation and Entropy of Ceria Oxide Using Topological Indices.

BACKGROUND: Cerium oxide nanoparticles (CeO2 NPs) have gained their importance as engineered nanomaterials (ENMs) that have wide applications as catalysts in industry, which direct to their prominent occurrence in natural and engineered water systems. Cerium oxide nanoparticles (CeO2 NPs) have gained their importance as engineered nanomaterials (ENMs) that have wide applications as catalysts in industry, which direct to their prominent occurrence in natural and engineered water systems. In wastewater treatment plants, CeO2 NPs can stay colloidally stable and be unconstrained in the secondary effluents. As they entered into tertiary treatment, such as advanced oxidation processes (AOPs), it is noteworthy that how the generated reactive oxygen species will change the colloidal stability, aggregation, and the surface chemistry of CeO2 NPs. AIM AND OBJECTIVE: The study was aimed to analyze the chemical graph of the crystal structure of Ceria Oxide(cuprite) CeO2. Also, our main objective is to compute the Heat of Formation and Entropy using degree based topological indices. MATERIALS AND METHODS: Chemical graph theory plays an important role in modeling and designing any chemical structure. The topological indices are the numerical invariants of a molecular graph and are very useful for predicting their physical properties. For calculation, we have utilized the combinatorial processing strategy, edge partition technique, vertex partition strategy, analytic procedures, graph hypothetical tools, degree counting technique and entirety of degrees of neighbor technique. Moreover, Matlab programming has been utilized for numerical computations and checks. We likewise utilized the maple for plotting these numerical outcomes. RESULTS: We have computed Heat of Formation and Entropy using degree based topological indices. Our main results are based on some degree based topological indices, namely, the atom bond connectivity index ABC, geometric arithmetic index GA, general Randi index, Forgotten index, Augmented zagreb index and Balban index for the chemical graph of the crystal structure of cuprite CeO2[p, q, t] We also provide a detailed application of the computed results. CONCLUSION: We discuss these indices exhibited difference with the reported heat of formation and entropy of cuprite CeO2[p, q, t] In almost all the cases, an exponential increase of aforementioned indices is observed with the increase in the number of cells or other words size of cuprite CeO2[p, q, t] nanocrystal. On the other hand, a linear relationship of indices with respect to the number of formula units suggests a slight modification of these indices for an appropriate explanation of the physical properties of cuprite CeO2[p, q, t] nanocrystal of varying size and hence its prospective application in nanoceria engineering.

Computation and Analysis of Topological Co-Indices for Metal-Organic Compound.

A topological descriptor is a mathematical illustration of a molecular construction that relates particular physicochemical properties of primary molecular structure as well as its mathematical depiction. Topological co-indices are usually applied for quantitative structure action relationships (QSAR) and quantitative structure property relationships (QSPR). Topological co-indices are topological descriptor which consider the noncontiguous vertex set. In this study, we studyied some of the accompanied renowned topological co-indices: the 1st and 2nd Zagreb co-indices, the 1st and 2nd multiplicative Zagreb co-indices, and the F-coindex. By applying structure based examinations and deductions, we discuss the earlier stated co-indices of few synthetic atomic structures that are frequently used in clinical, synthetic, and material designing.