Hifza Iqbal

Graph theory has become more significant in chemistry in recent years, especially when it comes to the study of molecular configurations. When molecules are depicted as graphs, with atoms serving as vertices and bonds as edges, a reliable technique for structural analysis is created. The circumcoronene bilayer germanium phosphide molecular graph is the main focus of this work, which uses topological invariants to estimate entropy. Combining numerical data with graphical representations for better interpretation strengthens the analysis even more. We closely study the entropy values at different points to understand the dynamic behavior of the molecules. By encouraging cutting-edge material production methods and technological applications, this interdisciplinary approach advances the material sciences and enhances our comprehension of quantitative structure–activity relationships and quantitative structure–property relationships analysis of circumcoronene.

Topological indices encode molecular structure into numerical descriptors, enabling prediction of physicochemical properties without extensive experimentation. This study evaluates the implementation of graph-theoretical topological indices in combination with multi-criteria decision-making methods to compute physicochemical properties and ranking of eye drugs. A set of classical topological indices, consisting of N SK1, N SK2, M1, M2, N M1, N M2, N SK, N F , and N H, are computed using an edge-partition approach to describe the structural aspects of 12 selected drugs. Multiple linear regression models were developed to develop quantitative structure–property relationship models for important physicochemical properties, including molar volume, polarizability, molar weight, and molar refraction. The multiple linear regression models showed reliable predictive output, with statistical indicators and correlation coefficients higher than 0.89, confirming the value of the selected indices. The VIKOR technique enables the ranking of drugs based on their estimated physicochemical properties. The combined application of quantitative structure–property relationship and multi-criteria decision-making framework enhances robustness in discriminating structurally similar eye drugs. This combination offers a systematic framework for prioritizing compounds in pharmacological research and drug optimization. Such approach also supports public health by facilitating more efficient drug development and therapeutic decision-making for eye diseases.

Colorectal cancer is challenging to treat because many anticancer drugs do not achieve optimal therapeutic effects. Moreover, these drugs can cause systemic side effects, and patients often respond differently to treatment. This study provides a computational framework that merges quantitative structure property relationship analysis with a computational methodology combining structural descriptors and ranking analysis to systematically analyze and rank 10 United States Food and Drug Administration approved medicines for colorectal cancer. A suite of degree-based and neighborhood degree-based topological indices were generated and examined for their association with essential physicochemical properties, specially molecular weight and molecular complexity. Correlation research revealed that specific degree-based indices, and neighborhood degree-based indices, exhibited strong predictive power for these properties. By employing ratio weighting alongside with the VIekriterijumsko Kompromisno Rangiranje and Technique for Order Preference by Similarity to Ideal Solution decision techniques, the medicines were ranked based on their predicted physicochemical performance. The results from both decision methods consistently showed fluorouracil as the highest ranked therapeutic agent, followed by tipiracil hydrochloride and bevacizumab, underlining their favorable structural and pharmacological properties. This comprehensive modelling technique provides a consistent and systematic strategy to aid in early-phase drug screening and inform decision-making in colorectal cancer therapy.

In this work, we employ a graph-theoretical framework to study the structural characteristics of nanocarbon sheets. Key auxiliary properties are predicted using the Van, R, and S topological indices, which makes it easier to design materials that are both energy-efficient and environmentally friendly. The analysis assesses how topological characteristics can affect performance metrics that are important for long-term uses in green energy systems. Our results show how useful these descriptors are for simulating the behavior of sustainable nanomaterials based on nanocarbons and directing the creation of devices with lower power consumption and higher energy efficiency. Theoretical expressions are clearly visualized by the use of tables and three-dimensional MATLAB figures.

A topological index is a numerical character associated with a graph that is invariant under graph isomorphism and describe the graphs topology. There are several graph operations that may be used to change it into a new structure, such as constructing a stellation, bounded dual, complement, subdivided, line graph, minor, dual, and medial. In this paper, we construct transformed networks from the concealled non-kekulean benzenoid hydrocarbon structure by applying stellation and bounded dual operations, further we study their degree based topological properties by appropriately labeling the graph. Degree based topological indices are playing significant role among other types of indices in chemical, pharmaceutical and bio-informatics industry, since they correlate the structure with its physicochemical properties.

Graph theory has great deal of application in disciplines like biology, computer science, informatics, engineering, mathematics, social science, linguistics and medicine. Topological indices are created by labeling the chemical structure through numerical parameters. These notations link chemical compounds physicochemical features such as boiling temperature, stability, strain energy etc, to its molecular structure. Different topological features of chemical structure have been explored. One of the molecular graphs topological indices are the connection indices defined on the number of connection between vertices of distance two. In this work, we compute the first Zagreb connection index, second Zagreb connection index, and modified first Zagreb connection index for hexagonal network and non kekulean benzenoid hydrocarbon.

A topological descriptor is regarded as a numerical parameter derived by using mathematical tools from the molecular graph of different chemical structures. The chemical graph theory is a paramount section of mathematical chemistry. In this section, there are many topological parameters, that have very useful characteristics to study the molecular structure of chemicals. In this article, we investigate topological indices of concealed non-kekulean benzenoid hydrocarbon graph. We will compute general Randic index, general sum connectivity index, sum connectivity index, general version of harmonic index, harmonic index, first, second and third Zagreb indices, SK, SK₁, SK₂ indices, augmented Zagreb index, atomic bond connectivity index, geometric arithmetic index, first and second gourava indices, first and second hyper-gourava indices and 4th version of atomic bond connectivity, 5th version of geometric arithmetic index, and the Sanskurti index.