On detour index of cycloparaphenylene and polyphenylene molecular structures

Abstract

Cycloparaphenylene is a particle that comprises a few benzene rings associated with covalent bonds in the para positions to frame a ring-like structure. Similarly, poly (para-phenylenes) are macromolecules that include benzenoid compounds straightforwardly joined to each other by C–C bonds. Because of their remarkable architectural highlights, these structures have fascinated attention from numerous vantage focuses. Descriptors are among the most fundamental segments of prescient quantitative structure-activity and property relationship (QSAR/QSPR) demonstrating examination. They encode chemical data of particles as quantitative numbers, which are utilized to create a mathematical correlation. The nature of a predictive model relies upon great demonstrating insights, yet additionally on the extraction of compound highlights. To a great extent, Molecular topology has exhibited its adequacy in portraying sub-atomic structures and anticipating their properties. It follows a two-dimensional methodology, just thinking about the interior plan, including molecules. Explicit subsets speak the design of every atom of topological descriptors. When all around picked, these descriptors give a unique method of describing an atomic system that can represent the most significant highlights of the molecular structure. Detour index is one such topological descriptor with much application in chemistry, especially in QSAR/QSPR studies. This article presents an exact analytical expression for the detour index of cycloparaphenylene and poly (para-phenylene).

Modified Detour Index of Hamiltonian Connected (Laceable) Graphs

“…That is, S n is attainable for every arbitrary pair of vertices. Also, we can see that S n has 4n(4n − 1) 2 Hamiltonian paths. Hence,…”

“…The detour index (1,2) of a connected graph G is defined as the sum of the detour distances (lengths of the longest paths) between unordered pairs of vertices of the graph. i.e…”

“…The detour index has important applications in chemistry. Applications of this parameter in quantitative structure activity and property relationship models were put forward in (2,3) . In (4) a comparative analysis with the Wiener index in terms of applicability in correlating structure boiling point of organic compounds.…”

Computational Analysis of Some More Rectangular Tessellations of Kekulenes and Their Molecular Characterizations

“…As a result, topological indices and their subsequent advances have received a lot of interest, and many papers are now devoted to the research of novel molecular descriptors and the associated computational techniques [ 29 , 40 , 41 , 42 , 43 , 44 , 45 , 46 , 47 ]. Some further works on topological indices and related topics can be seen in [ 48 ]; we can extend our future works to these areas [ 49 , 50 , 51 , 52 ], and numerous similar issues can be solved if new topological indices are defined or modified. Through the use of strength-weighted graphs, this study establishes the topological characterization of rectangular kekulene meshes Type I and II using a variety of Bond additive, distance-based, distance- and degree-based, associated topological descriptors, thus enhancing our understanding of the numerous chemical and physical characteristics of these compounds, such as their aromaticity, topological resonance energy, ring current diamagnetism, and the functions performed by graph-theoretical internal substructures like conjugated circuits.…”