Square-heptagonal kink chains are important polygonal structures in chemical graph theory with relevance to materials science, nanotechnology, and engineering. In these chains, kinks arise when the local arrangement of square and heptagonal units causes a deviation from linearity. This paper introduces and investigates three new configurations of type H2,2 square-heptagonal kink chains, denoted by H2,21 ${H}_{2,2}^{1}$ , H2,22 ${H}_{2,2}^{2}$ , and H2,23 ${H}_{2,2}^{3}$ . For these structures, we derive vertex and edge partitions and obtain closed-form expressions for several degree-based topological descriptors, including the forgotten, first Zagreb, second Zagreb, geometric-arithmetic, sum-connectivity, and atom-bond connectivity descriptors. Both odd and even numbers of kinks are considered to provide complete analytical results. Numerical comparisons are also presented to examine how different kink configurations influence descriptor values. The results highlight the structural distinctions among the proposed kink chains and provide useful mathematical tools for studying complex polygonal networks with potential applications in molecular modeling and nanomaterial analysis.
Two new Zn(II)/Cd(II) complexes, [Zn(L)(cba)]n (1) and [Cd(L)(Br)2]& centerdot;H2O (2) (L = 2-(4-fluoro-phenyl)-1H-imidazo[4,5-f][1,10]phenanthroline, H2cba = 4-Carboxyphenoxyacetic acid), have been synthesized hydrothermally and their structures and properties were systematically analyzed and characterized. 1 is composed of the [Zn(L)(cba)] unit, each deprotonated 4-cba2- ligand chelates a Zn(II) atom, forming a 1D chain structure. The 1D double-chain structure is further formed through the pi-pi stacking interactions between L ligands. In addition, 2 is composed of the [Cd(L)(Br)2] unit. The molecule is further extended into a 1D supramolecular chain via the interactions between nitrogen-containing ligands, and the 1D chain structure is further stabilized by hydrogen bonding interactions.
The present work explores the correlation between the values of the heat of formation (HOF) and topological indices of hydrogen boride (B2H6), which is a compound having an unique electron-deficient molecular structure. Topological indices play a significant role in mathematical chemistry by providing numerical descriptors that reflect the structural characteristics of molecular networks and their physicochemical behavior. The current study applies sophisticated curve fitting algorithms to quantitatively assess reverse degree-based topological indices and their correlation with the heat of formation HOF for the hydrogen boride network (B2H6). To find out how well they predicted thermochemical stability, a number of reverse indices were calculated, such as the reverse Zagreb indices, reverse Balaban index, and reverse forgotten index. To construct precise mathematical correlations between each topological index and the related HOF values, nonlinear curve fitting models were created. Additionally, the combination of statistical and computational methods offers a dependable and effective framework for investigating structure-property connections in boron-based nano structures. This approach can be expanded to additional molecular systems to improve materials science and chemical graph theory predictive modeling.
Topological indices serve as important molecular descriptors in quantitative structure-property relationship (QSPR) and quantitative structure-activity relationship (QSAR) studies. In this work, we present a comprehensive topological analysis of four molecular structures based on the leap versions of several Zagreb indices. The mathemat ical formulations are accompanied by numerical evalua tions and graphical illustrations, providing systematic insights into the structural properties of these chemical networks. The obtained analytical expressions provide structural descriptors that encode second neighborhood information of the considered molecular networks and may support future QSPR/QSAR modeling and comparative structural analysis of nanostructures.
Topological indices play a central role in mathematical chemistry for correlating structural features of molecular graphs with physicochemical properties. Motivated by limitations of existing degree and distance-based descriptors, we introduce a novel connectivity index that counts the d-neighbors (vertices whose distance equals their degree in a connected molecular graph). This new descriptor, called the d-connectivity index, extends classical connectivity frameworks. We establish fundamental theoretical results, including lower bounds, relationships with the first Zagreb index, and expressions for subdivision graphs and graphs of small diameter. Furthermore, we compute and compare the d-connectivity index with six widely used indices for three hexa-organic molecular structures. The findings highlight strong structural sensitivity and the potential applicability of the proposed index in QSPR/QSAR modelling. Moreover, the chemical relevance of the d-connectivity index is established through strong polynomial correlations with multiple physicochemical properties of benzenoid hydrocarbon compounds and octane isomers, confirming its effectiveness as a predictive molecular descriptor.
