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The interdependency of the molecular structures of drugs and their biomedical characteristics have already been proved by lab experiments. We can approximate these characteristics by computing numerical invariants associated to their molecular structures. These invariants are called topological indices. Among many topological indices, the face index (FI) is defined most recently. The FI may be helpful in approximating the boiling point and π‐electron energy of benzenoid hydrocarbons and some other drugs with the correlation coefficient r>.99. In this article, we compute the FI for Boron triangular nanotubes, the nanotubes VC5V7p,q and HC5C7p,q, Also compute the FI for quadrilateral sections cut from regular hexagonal lattice Pmn and Pm+1/2n. [ABSTRACT FROM AUTHOR]

Several graph invariants have been defined and studied, which present applications in nanochemistry, computer networks, and other areas of science. One vastly studied class of the graph invariants is the class of the topological indices, which helps in the studies of chemical, biological, and physical properties of a chemical structure. One recently introduced graph invariant is the face index, which can assist in predicting the energy and the boiling points of the certain chemical structures. In this paper, we drive the analytical closed formulas of face index of silicon carbides S i 2 C 3 − I a , b , S i 2 C 3 − II a , b , S i 2 C 3 − III a , b , and S i C 3 − III a , b . [ABSTRACT FROM AUTHOR]

A novel topological index, the face index ( F I ), is proposed in this paper. For a molecular graph G, face index is defined as F I (G) = ∑ f ∈ F (G) d (f) = ∑ v ∼ f , f ∈ F (G) d (v) , where d (v) is the degree of the vertex v. The index is very easy to calculate and improved the previously discussed correlation models for π - e l e c t r o n energy and boiling point of benzenoid hydrocarbons. The study shows that the multiple linear regression involving the novel topological index can predict the π -electron energy and boiling points of the benzenoid hydrocarbons with correlation coefficient r > 0.99 . Moreover, the face indices of some planar molecular structures such as 2-dimensional graphene, triangular benzenoid, circumcoronene series of benzenoid are also investigated. The results suggest that the proposed index with good correlation ability and structural selectivity promised to be a useful parameter in QSPR/QSAR. [ABSTRACT FROM AUTHOR]

Irregularity indices are usually used for quantitative characterization of the topological structures of non-regular graphs. In numerous problems and applications, especially in the fields of chemistry and material engineering, it is useful to be aware of the irregularity of a molecular structure. Furthermore, the evaluation of the irregularity of graphs is valuable not only for quantitative structure-property relationship (QSPR) and quantitative structure-activity relationship (QSAR) studies but also for various physical and chemical properties, including entropy, enthalpy of vaporization, melting and boiling points, resistance, and toxicity. In this paper, we will restrict our attention to the computation and comparison of the irregularity measures of different classes of dendrimers. The four irregularity indices which we are going to investigate are σ irregularity index, the irregularity index by Albertson, the variance of vertex degrees, and the total irregularity index. [ABSTRACT FROM AUTHOR]

A chemical compound can be represented as a chemical graph. A topological index of a (chemical) graph is a numeric value of a graph which characterize its topology and is usually graph invariant. The Zagreb indices, Randic index and sum-connectivity indices are useful in the study of antiinflammatory activities, boiling point, molecular complexity heterosystems of certain chemical instances, and in elsewhere. In this paper, we calculate the mentioned topological indices of some infinite classes of prophyrin dendrimers. [ABSTRACT FROM AUTHOR]