The most general algebraic polynomial to obtain a massive number of degree-based topological indices for a specific family of structures is the M-polynomial. In this paper, the M-polynomial of some graph operations was derived including join, corona product, strong product, tensor product, splice, and link of regular graphs. By using those expressions, numerous degree-based indices of the aforesaid operations were computed. The explicit expressions of the indices were also derived for some particular graphs.

The Bertz indices, derived by counting the number of connecting edges of line graphs of a molecule were used in deriving the QSPR models for the physicochemical properties of alkanes. The inability of these indices to identify the hetero centre in a chemical compound restricted their applications to hydrocarbons only. In the present work, a novel molecular descriptor has been derived from the weighted line graph of the molecular structure and applied in correlating the physicochemical properties of alkane isomers with these descriptors. A weight is tagged at the vertex of the line graph, which consequently modifies the weight of the edge. These descriptors were found to classify the alkane isomers and served well in deriving the QSPR models for various physicochemical properties. The mathematical calculations include the quantitative treatment on the role of substituents (alkyl) in governing the properties under study of the alkane isomers. Further, the use of weighted line graph in the enumeration of the topological index opens up a new vista on application to heteroatomic systems.

By using molecular farming, plants are used as a bio-reactor for producing low cost recombinant proteins. This technology had been successful in the production of primary products in the commercial field. Other recombinant products are in final steps of production. In the last 10 years, up to 100 different recombinant proteins are produced in transgenic plants. Plants have many advantages in comparison with other expression systems, especially in economic, safety, operations and production aspects. However, there are some problems for using plants as a bio-reactor with the goal of recombinant proteins production that should be considered. Some of these problems are: the quality of final product, extraction and the processing of plant derived pharmaceutical macromolecules and bio-safety. In this study, we will review the global view of molecular farming and some successful cases in Iran. During 8 years of research in the field of molecular farming in Iran, especially in Tarbiat Modarres University, different kinds of recombinant proteins such as VHH single domain antibody in tobacco and canola and tPA protein in tobacco were expressed. The human gamma interferon in canola and tobacco and also the luciferase enzyme in tobacco, African violet and canola were produced. Also, useful projects are executed in the field of transplastomic plants in order to express the mentioned genes in the chloroplast. In transferring the human pro-insulin gene to chloroplast genome, this gene was bombarded onto tobacco leaf ex-plants using a particle delivery system. Leaf ex-plants produced adventitious shoots when cultured on shoot-inducing medium containing spectinomycin. The results of peR confirmed that the pro-insulin gene was present in the chloroplast genome.

The insurance industry plays a vital role in economic stability and risk management. This study aims to forecast the return on assets (ROA) in Iran’s insurance sector using the Bayesian Structural Time Series (BSTS) model, while identifying key macroeconomic drivers via the TVP-Graph approach. Based on time-series data from 2011 to 2024, findings indicate that capital adequacy and financial leverage are the most influential factors on ROA, whereas unemployment has no significant effect. The 24-month forecast suggests relatively stable yet fragile financial performance, highlighting a high degree of uncertainty and the need for structural and policy reforms.

Mathematical chemistry is a branch of theoretical chemistry that studies molecular structure without considering their quantum mechanics using mathematical methods. Carbon nanotubes are a particular type of fullerenes. In this article, K-Banhatti indices are obtained with the help of K-Banhatti polynomials for the molecular graph and the line graph of the TUC4C8(S) nanotube. Next, first, the (a, b)- Nirmala index is calculated for the molecular graph and line graph of TUC4C8(S) nanotube, and then using them, Y-index and some topological indices are computed.

The independence graph Ind(G) of a graph G is the graph with vertices as maximum independent sets of G and two vertices are adjacent, if and only if the corresponding maximum independent sets are disjoint. In this work, we find the independence graph of Cartesian product of d copies of complete graphs Kq, which is known as the Hamming graph H(d, q). Greenwell and Lovasz [7] found that the independence number of direct product of d copies of Kq as qd−1. We prove that the independence number of Hamming graph H(d, q), which is cartesian product of d copies of Kq, is also qd−1. As an application of our findings, we find answers for rook problem in higher dimensional square chess board.

In addition to his countless contributions to spectral graph theory, some works of Dragoš Cvetkovic are concerned with chemical problems. These are briefly outlined, with emphasis on his collaboration with the present author.

In this paper, we find the star chromatic number of central graph of complete bipartite graph and corona graph of complete graph with path and cycle.