This study explores how graph-based models can be used to predict key electronic properties of molecular structures, particularly benzenoid hydrocarbons as hexagonal systems. By focusing on temperature-related indices that reflect how atoms are connected within a molecule, the authors apply an optimization approach to identify the most optimal variants of these indices. The results show that these refined descriptors offer strong potential for accurately estimating total -electron energy. This work resolves two open questions in the field and supports the broader application of such indices in chemical property prediction and materials design.
Cheminformatics is the field that combines chemistry with data science and computational techniques to store, analyze, and predict chemical information, particularly through the use of digital representations of molecular structures. This discipline is crucial in areas like drug discovery, materials science, and toxicology, where it enables efficient analysis of chemical data and accelerates research and development processes. Quantitative Structure-Property Relationship (QSPR) modeling is a cheminformatics technique that uses mathematical and statistical methods to correlate molecular structures with their physical, chemical, or biological properties. By predicting properties based on molecular descriptors, QSPR aids in the efficient design and optimization of new compounds in fields like pharmaceuticals and materials science, and drug design.
Mathematical chemistry applies mathematical techniques to solve chemical problems, with QSPR modeling as a key area where it quantifies the relationship between molecular structure and characteristics. As a subbranch of mathematical chemistry, chemical graph theory utilizes graph theory to represent and analyze chemical structural configurations, where atoms and bonds are modeled as vertices and edges. This approach allows researchers to derive topological indices and descriptors that correlate with chemical properties, aiding in the prediction of molecular behavior and properties in areas like environmental chemistry, materials science, and drug design. Topological indices and descriptors in chemical graph theory are numerical values retrieved from molecular representations, capturing structure's information such as size, shape, and branching. On the prediction of chemical, biological and physical characteristics of bio-molecular structures and nanostructures by mean of QSPR, the reader is being referred to. Graph theory has diverse applications in scientific areas such as cellular Internet of Things, multiuser mobile edge computing systems, topological neural network, downlink communications systems, and distributed edge networks.
Temperature-based graphical indices are topological indices calculated using the temperatures of vertices in a graph, representing the atoms' connectivity within molecules. Temperature-based indices are essential in QSPR studies as they provide a simple yet effective way to quantify the structural properties of molecules. Common temperature-based invariants, such as the hyper temperature index, sum-connectivity indices, and the Sombor temperature index, have been shown to correlate well with a diverse set of physicochemical characteristics, including boiling point, heat capacity, and the total -electron energy (). Their ability to encapsulate key structural features makes them valuable tools for the prediction of various chemical, biological and physical characteristics of compounds in environmental chemistry, materials science, and drug design.
A contemporary area of research involves conducting comparative analyses of various graphical indices to identify the most efficient ones with strong predictive capabilities, while excluding those with poor performance to prevent their use in future studies. For instance, Gutman & Tošović conducted a comparative analysis on degree-based indices and showed that the augmented Zagreb index, delivering the strongest estimation ability regarding physical and chemical characteristics of alkanes, deserves further attention in QSPR modeling. Hayat et al. extended the work of Gutman & Tošović from physicochemical properties (PCPs) of alkanes to of polycyclic hydrocarbons. Hayat et al. (resp. Malik et al.) considered distance-based (resp. eigenvalues-based) graphical indices for a comparative analysis to determine their prediction ability for of BHs. Recently, Hayat and Liu conducted a similar study for temperature-based graphical indices. In their study, Hayat and Liu considered the first and second general temperature index only for . Both and performed exceptionally motivating Hayat and Liu to pose the following two problems: (Hayat and Liu)
The motivation of this work comes from the fact the first and second general temperature indices with specific values of correlate well with of lower BHs. This naturally raises the two open problems 1.1 and 1.2. The problem statement of this work is the aim to identify the optimal form of two general temperature indices by determining the values of that maximize their correlation with -electron energy, thereby resolving Problems 1.1 and 1.2. This leads to the objective of this research to solve the two open problems by implementing contemporary tools such as combinatorial optimization and regression analysis. The novelty of this research lies in the use of combinatorial optimization to determine the most effective form of temperature-based graph indices for predicting -electron energy. Unlike previous studies limited to fixed parameter values, this work identifies optimal configurations across a continuous range, offering a more accurate and generalizable approach to molecular property prediction.