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Cyclooctane is classified as a cycloalkane, characterized by the chemical formula C 8 H 16 . It consists of a closed ring structure composed of eight carbon atoms and sixteen hydrogen atoms. A cyclooctane chain typically refers to a series of cyclooctane molecules linked together. Cyclooctane and its derivatives find various applications in chemistry, materials science, and industry. Topological indices are numerical values associated with the molecular graph of a chemical compound, predicting certain physical or chemical properties. In this study, we calculated the expected values of degree-based and neighborhood degree-based topological descriptors for random cyclooctane chains. A comparison of these topological indices' expected values is presented at the end., Competing Interests: The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest., (Copyright © 2024 Jing, Yousaf, Farhad, Tchier and Aslam.)

Brahmi Nei (BN), a traditional Indian polyherbal formulation has been described in classical texts for the treatment of anxiety and depression, as well as to fortify the immune system. The individual herbs of BN have been used for treatment of wide range of disorders including cognition, inflammation, skin ailments and cancer etc., This diverse basket of therapeutic activity suggests that BN may possess therapeutic benefits to other disorders. So, the present study aims to identify the potential therapeutic targets of BN using a network pharmacological approach to comprehend the multi target action of its multiple phytoconstituents. We have employed Randić Index for the first time to calculate the contribution score of module segregated targets towards diseases. Our results suggests that BN targets could also be effective in other diseases such as lysosomal storage disorders, respiratory disorders etc., apart from neurological disorders. The key targets with highest topological measures of Targets-(Pathway)-Targets network were identified as potential therapeutic targets of BN. And the top hit target PTGS2, a gene encoding for cyclooxygenase-2 was further evaluated using molecular docking, molecular dynamic simulation and in vitro studies. Our findings open up new therapeutic facets for BN that can be explored systematically in future.Communicated by Ramaswamy H. Sarma.

We assume that D is a directed graph with vertex set V ( D ) = { v 1 , … v n } and arc set E ( D ) . A VDB topological index φ of D is defined as φ ( D ) = 1 2 ∑ u v ∈ E ( D ) φ d u + , d v - , where d u + and d v - denote the outdegree and indegree of vertices u and v , respectively, and φ i , j is a bivariate symmetric function defined on nonnegative real numbers. Let A φ = A φ ( D ) be the n × n general adjacency matrix defined as [ A φ ] i j = φ d v i + , d v j - if v i v j ∈ E ( D ) , and 0 otherwise. The energy of D with respect to a VDB index φ is defined as E φ ( D ) = ∑ i = 1 n σ i ( A φ ) , where σ 1 ( A φ ) ≥ σ 2 ( A φ ) ≥ ⋯ ≥ σ n ( A φ ) ≥ 0 are the singular values of the matrix A φ . We will show that in case φ = R is the Randić index, the spectral norm of A R is equal to 1, and rank of A R is equal to rank of the adjacency matrix of D . Immediately after, we illustrate by means of examples, that these properties do not hold for most well-known VDB topological indices. Taking advantage of nice properties the Randić matrix has, we derive new upper and lower bounds for the Randić energy E R in digraphs. Some of these generalize known results for the Randić energy of graphs. Also, we deduce a new upper bound for the Randić energy of graphs in terms of rank, concretely, we show that E R ( G ) ≤ r a n k ( G ) for all graphs G , and equality holds if and only if G is a disjoint union of complete bipartite graphs., Competing Interests: The authors declare no conflict of interest., (© 2022 The Authors.)

Chemical descriptors are numeric numbers that capture the whole graph structure and comprise a basic chemical structure. As a topological descriptor, it correlates with certain physical aspects in addition to its chemical representation of underlying chemical substances. In the modelling and design of any chemical network, the graph is important. A number of chemical indices have been developed in theoretical chemistry, including the Wiener index, the Randić index, and many others. In this paper, we look at the benzenoid networks and calculate the exact topological indices based on the degrees of the end vertices.

In this article, we study the degree-based topological indices in a random polyomino chain. The key purpose of this manuscript is to obtain the asymptotic distribution, expected value and variance for the degree-based topological indices in a random polyomino chain by using a martingale approach. Consequently, we compute the degree-based topological indices in a polyomino chain, hence some known results from the existing literature about polyomino chains are obtained as corollaries. Also, in order to apply the results, we obtain the expected value of several degree-based topological indices such as Sombor, Forgotten, Zagreb, atom-bond-connectivity, Randić and geometric-arithmetic index of a random polyomino chain.

Background: The valency of an atom in a molecular structure is the number of its neighboring atoms. A large number of valency based molecular invariants have been conceived, which correlate certain physio-chemical properties like boiling point, stability, strain energy and many more chemical compounds., Objective: Our aim is to study the valency based molecular invariants for four hexa chemical structures, namely hexagonal network, honeycomb network, oxide network and silicate sheet network., Methods: We use the technique of atom-bonds partition according to the valences of atoms to find results., Results and Conclusion: Exact values of valency-based molecular invariants, namely the Randi index, atom bond connectivity index, geometric arithmetic index, harmonic index, Zagreb indices, Zagreb polynomials, F-index and F-polynomial, are found for four hexa chemical structures., (Copyright© Bentham Science Publishers; For any queries, please email at epub@benthamscience.net.)

Topological indices are numerical parameters used to study the physical and chemical properties of compounds. In quantitative structure⁻activity relationship QSARs, topological indices correlate the biological activity of compounds with their physical properties like boiling point, stability, melting point, distortion, and strain energy etc. In this paper, we determined the M-polynomials of the crystallographic structure of the molecules Cu₂O and T i F₂ [ p,q,r ]. Then we derived closed formulas for some well-known topological indices using calculus. In the end, we used Maple 15 to plot surfaces associated with the topological indices of Cu₂O and T i F₂ [ p,q,r ]., Competing Interests: The authors declare no conflicts of interest.