Analyzing the expected values of neighborhood degree-based topological indices in random cyclooctane chains.

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.

Exploring expected values of topological indices of random cyclodecane chains for chemical insights.

Chemical graph theory has made a significant contribution to understand the chemical compound properties in the modern era of chemical science. At present, calculation of the topological indices is one of most important area of research in the field of chemical graph theory. Cyclodecane is a cyclic hydrocarbon with the chemical formula C 10 H 20 . It consists of a ring of ten carbon atoms bonded together in a cyclical structure. Cyclodecane chains can be part of larger molecules or polymers, where multiple cyclodecane rings are connected together. These molecules can have various applications in chemistry, materials science, and pharmaceuticals. This article aims to determine expected values of some connectivity based topological indices of random cyclodecane chains, containing saturated hydrocarbons with at least two rings. It also compares these descriptors using explicit formulae, numerical tables and present graphical profiles of these comparisons.

Computation of expected values of some connectivity based topological descriptors of random cyclooctane chains.

Cyclooctane is a cycloalkane consisting of carbon and hydrogen atoms arranged in a closed ring structure. Cyclooctane chains can be found in various organic compounds and are significant in the field of organic chemistry due to their diverse reactivity and properties. The atom-bond connectivity index ( A B C ), the geometric-arithmetic index ( G A ), the arithmetic-geometric index ( A G ) and the forgotten index ( F ) are four well-studied molecular descriptors that have found applications in QSPR and QSAR studies. These topological descriptors have shown significant correlations with different physiochemical properties of octane isomers. In this work, the expected values of four degree based topological descriptors for random cyclooctane chains are calculated. An analytical comparison is given between the expected values of A B C , G A , A G , and F indices of random cyclooctane chains.

Investigation for metallic crystals through chemical invariants, QSPR and fuzzy-TOPSIS.

Chemical graph theory has revolutionary impacts in the field of mathematical chemistry when complex structures are investigated through various chemical invariants (topological indices). We have performed evaluations by considering alternatives as crystal structures, namely Face-Centered Cubic (FCC), hexagonal close-packed (HCP), Hexagonal (HEX), and Body Centered Cubic (BCC) Lattice structures, through the study of two-dimensional degree-based chemical invariants, which we considered criteria. QSPR modeling has been implemented for the targeted crystal structures to investigate the ability of targeted chemical invariants to predict targeted physical properties. Furthermore, the Fuzzy-TOPSIS technique provides the optimal structure HCP ranking as first among all structures when investigated under more than one criterion, which justifies further that the structure attaining dominant countable invariant values ranks high when investigated through physical properties and fuzzy TOPSIS.Communicated by Ramaswamy H. Sarma.

Multiple-Criteria Decision-Making (MCDM) techniques to study the behavior of dendrimers using topological indices.

Topological indices provide a mathematical language for capturing molecular structure, symmetry, and predicting properties. Dendrimers are microscopic bilaterally symmetrical molecules with a well-defined homogeneous nanoparticles structure, often consisting of a symmetric center, inner shell, and outer shell. In this work, first we compute some degree-based topological indices of Porphyrin (DnPn),Poly (Propyl) Ether Imine(PETIM), Zinc porphyrin (DPZn), and Polyamidoamine (PAMAM) dendrimers. Then, we use multi-criteria decision making (MCDM) techniques to establish the weighted evaluation of dendrimer classes based on certain topological indices. For weighted analysis we correlate the properties of benzene derivatives with topological invariants. Finally, based on the multi-criteria decision making techniques namely TOPSIS, SAW and MOORA method, we have ranked the dendrimer structures based on their properties.

Metric and fault-tolerant metric dimension for GeSbTe superlattice chemical structure.

The concept of metric dimension has many applications, including optimizing sensor placement in networks and identifying influential persons in social networks, which aids in effective resource allocation and focused interventions; finding the source of a spread in an arrangement; canonically labeling graphs; and inserting typical information in low-dimensional Euclidean spaces. In a graph G, the set S⊆V(G) of minimum vertices from which all other verticescan be uniquely determined by the distances to the vertices in S is called the resolving set. The cardinality of the resolving set is called the metric dimension. The set S is called fault-tolerant resolving set if S\{v} is still a resolving set of G. The minimum cardinality of such a set S is called fault-tolerant metric dimension of G. GeSbTe super lattice is the latest chemical compound to have electronic material that is capable of non-volatile storing phase change memories with minimum energy usage. In this work, we calculate the resolving set (fault tolerant resolving set) to find the metric dimension(fault-tolerant metric dimension) for the molecular structure of the GeSbTe lattice. The results may be useful in comparing network structure and categorizing the structure of the GeSbTe lattice.

Implementing QSPR modeling via multiple linear regression analysis to operations research: a study toward nanotubes.

Chemical graph theory significantly predicts multifarious physio-chemical properties of complex and multidimensional compounds when investigated through topological descriptors and QSPR modeling. The targeted compounds are widely studied nanotubes attaining exquisite nanostructures due to their distinguishable properties attaining numeric values. The studied nanotubes are carbon, naphthalene, boron nitride, V-phenylene, and titania nanotubes. In this research work, these nanotubes are characterized through their significance level by implementing highly applicable MCDM techniques. TOPSIS, COPRAS, and VIKOR are used to perform a comparative analysis between them through each optimal ranking. The criteria originated from multiple linear regression modeling established between degree-based topological descriptors and the physio-chemical properties of each nanotube.

Targeting highly resisted anticancer drugs through topological descriptors using VIKOR multi-criteria decision analysis.

The disease cancer is expanding on high spans in virtually all over the world, and undoubtedly, the research through all the aspects of sciences for each of its perspective is a great cause in reducing its severeness and symptoms. Chemotherapy is itself a cure to cancer as it helps in controlling the formation of cancerous cells but leaving multiple side effects on a human body. In this research work, we targeted 21 anticancer drugs that are in taken by the patients in combinations during chemotherapies. We introduce another branch of mathematics named as OR (Operations Research) linking to the chemical graph theory. Chemical graph theory allows us to generate highly resistant research on any structure via quantitative structure property relationship (QSPR) modeling to explore and develop new compounds for drugs. In this research study, we visualized what else the QSPR could provide when it comes to ranking drugs. We visualized the results obtained for boiling points and enthalpy of vaporizations through QSPR as the values of correlation coefficients and the errors generated under unique QSPR modeling. The implementation of VIKOR provides the best ranking for each of anticancer drugs when keeping in concern the specified properties, and the conclusions from this research work show another path to biologist scientists to create best combinations keeping in concern the study generated from QSPR. Supplementary Information: The online version contains supplementary material available at 10.1140/epjp/s13360-022-03469-x.

On Trees with Greatest F-Invariant Using Edge Swapping Operations.

The F-index of a graph Q is defined as F(Q)=∑ t∈V(Q)(d t )3. In this paper, we use edge swapping transformations to find the extremal value of the F-index among the class of trees with given order, pendent vertices, and diameter. We determine the trees with given order, pendent vertices, and diameter having the greatest F-index value. Also, the first five maximum values of F index among the class of trees with given diameter are determined.

Study of HCP (Hexagonal Close-Packed) Crystal Structure Lattice through Topological Descriptors.

Chemical graph theory is a multidisciplinary field where the structure of the molecule is analyzed as a graphical structure. Chemical descriptors are one of the most important ideas employed in chemical graph theory; this is to associate a numerical value with a graph structure that often has correlation with corresponding chemical properties. In this paper, we investigate another very important closed-packed usual crystal structure defined as HCP (Hexagonal Close-Packed) crystal structure and its lattice formed by arranging its unit cells in a dimension for topological descriptors based on a neighborhood degree, reverse degree, and degree. Furthermore, we classify which descriptor is more dominating.

Hosoya Polynomial for Subdivided Caterpillar Graphs.

BACKGROUND: Computing Hosoya polynomial for a graph associated with a chemical compound plays a vital role in the field of chemistry. From Hosoya polynomial, it is easy to compute the Weiner index(Weiner number) and Hyper Weiner index of the underlying molecular structure. The Wiener number enables the identifying of three basic features of molecular topology: branching, cyclicity, and centricity (or centrality) and their specific patterns, which are well reflected by the physicochemical properties of chemical compounds. Caterpillar trees are used in chemical graph theory to represent the structure of benzenoid hydrocarbons molecules. In this representation, one forms a caterpillar in which each edge corresponds to a 6-carbon ring in the molecular structure, and two edges are incident at a vertex whenever the corresponding rings belong to a sequence of rings connected end-to-end in the structure. Due to the importance of Caterpillar trees, it is interesting to compute the Hosoya polynomial and the related indices. METHODS: The Hosoya polynomial of a graph G is defined as H(G;x) = Σd(G)K=0 d(G.k)xk. In order to compute the Hosoya polynomial, we need to find its coefficient d(G.k) which is the number of pairs of vertices of G which are at distance k. We classify the ordered pair of vertices which are at distance , 2 ≤ m ≤ (n + 1)k in the form of sets. Then finding the cardinality of these sets and adding them up will give us the value of coefficient d(G.m) . Finally, using the values of coefficients in the definition, we get the Hosoya polynomial of uniform subdivision of caterpillar graph. RESULT: In this work, we compute the closed formula of Hosoya polynomial for subdivided caterpillar trees. This helps us to compute the Weiner index and hyper-Weiner index of uniform subdivision of caterpillar graph. CONCLUSION: Caterpillar trees are among the important and general classes of trees. Thorn rods and thorn stars are the important subclasses of caterpillar trees. The idea of the present research article is to provide a road map to those researchers who are interested in studying the Hosoya polynomial for different trees.

Pakistan Oral Cancer Collaborative: analyzing barriers and obstacles to oral cancer diagnosis, treatment, and prevention in Pakistan.

Oral cancer is a global health problem with increasing case numbers worldwide and no significant improvement in prognosis over the last few decades. It is one of the most common cancers and a leading cause of death in Pakistan, although the number reported is significantly underreported owing to the lack of a national cancer repository, and the true magnitude of this challenge is not known. Bilateral discussions and workshops funded by the Global Challenges Research Fund brought together a number of like-minded researchers and clinicians from the United Kingdom and Pakistan to analyze the status quo and plan the future course. This article reviews some of these discussions as well as barriers to oral cancer diagnosis in Pakistan and makes recommendations to investigate the magnitude and develop measures that may help tackle this devastating disease.

Preparedness and impact of COVID 19 infection at tertiary care neurology centers in Pakistan.

OBJECTIVE: We aimed to assess the response and impact of covid 19 pandemic at tertiary care centers in Pakistan especially pertaining to neurological care, facilities and training. METHODS: A pre-tested survey form was sent to 40 neurology tertiary care centers in all the provinces in the country in the first week of July 2020. 33 filled forms were received, out of which 18 were public (government) and 15 were private hospitals. RESULTS: Estimated 1300 HCW (faculty, medical officers, trainees and nurses) work at these 33 participating centers. There were 17 deaths among HCW (1.3%) at ten centers. Sufficient personal protective equipment (PPE) were provided to 158 HCW (12%). 129 (10%)HCW tested positive for COVID 19 at 31 centers including trainees/medical officers (39), consultants (29) and nursing and other staff (61). Due to low neurology admissions, 23/33 hospitals (70%) posted neurology trainees in COVID 19 units to contribute to covid care. Less than 50% hospitals did covid screening PCR before admission to neurology wards. Only 10% hospitals provide training and regular update to HCW. Neurology tele-health services were started for clinically stable patients at 15 (45%) centers. Only 60% neurology training programs were able to start online training. Ongoing research studies and trials focusing neurological manifestations of COVID-19 were done at 10 (30%) centers. Modification of facilities for COVID patients showed that 24(72%) hospitals strictly reduced the number of attendants accompanying patients. Only 10 (30%) centers had neurophysiological tests being conducted on COVID-19 patients. Mental health support services to HCW were provided at 12 (36%) centers. CONCLUSIONS: Among HCW 10% tested positive for covid and 1.3% died. Mental health support services offered for HCW were available in 36% institutions. Neurology training was substantially affected due to low admissions, limited ward rounds and limited availability of online training.

n-polynomial exponential type p-convex function with some related inequalities and their applications.

In this paper, the idea and its algebraic properties of n-polynomial exponential type p-convex function have been investigated. Authors prove new trapezium type inequality for this new class of functions. We also obtain some refinements of the trapezium type inequality for functions whose first derivative in absolute value at certain power are n-polynomial exponential type p-convex. At the end, some new bounds for special means of different positive real numbers are provided as well. These new results yield us some generalizations of the prior results. Our idea and technique may stimulate further research in different areas of pure and applied sciences.

Bio-inspired Analytical Heuristics to Study Pine Wilt Disease Model.

This paper portrays the dynamics of pine wilt disease. The specific formula for reproduction number is accomplished. Global behavior is completely demonstrated on the basis of the basic reproduction number [Formula: see text]. The disease-free equilibrium is globally asymptotically stable for [Formula: see text] and in such a case, the endemic equilibrium does not exist. If [Formula: see text] exceeds one, the disease persists and the unique endemic equilibrium is globally asymptotically stable. Global stability of disease-free equilibrium is proved using a Lyapunov function. A graph-theoretic approach is applied to show the global stability of the unique endemic equilibrium. Sensitivity analysis has been established and control strategies have been designed on the basis of sensitivity analysis.

On eccentricity-based topological descriptors of water-soluble dendrimers.

Previous studies show that certain physical and chemical properties of chemical compounds are closely related with their molecular structure. As a theoretical basis, it provides a new way of thinking by analyzing the molecular structure of the compounds to understand their physical and chemical properties. The molecular topological indices are numerical invariants of a molecular graph and are useful to predict their bioactivity. Among these topological indices, the eccentric-connectivity index has a prominent place, because of its high degree of predictability of pharmaceutical properties. In this article, we compute the closed formulae of eccentric-connectivity-based indices and its corresponding polynomial for water-soluble perylenediimides-cored polyglycerol dendrimers. Furthermore, the edge version of eccentric-connectivity index for a new class of dendrimers is determined. The conclusions we obtained in this article illustrate the promising application prospects in the field of bioinformatics and nanomaterial engineering.

On Eccentricity-Based Topological Indices Study of a Class of Porphyrin-Cored Dendrimers.

It is revealed from the previous studies that there is a strong relation between the chemical characteristic of a chemical compound and its molecular structure. Topological indices defined on the molecular structure of biomolecules can help to gain a better understanding of their physical features and biological activities. Eccentricity connectivity indices are distance-based molecular structure descriptors that have been used for the mathematical modeling of biological activities of diverse nature. As the porphyrin has photofunctional properties, such as a large absorption cross-section, fluorescence emission, and photosensitizing properties, due to these properties, porphyrin dendrimers can be used as photofunctional nanodevices. In this paper, we compute the exact formulae of different versions of eccentric connectivity index and their corresponding polynomials for a class of porphyrin-cored dendrimers. The results obtained can be used in computer-aided molecular design methods applied to pharmaceutical engineering.

On Forgotten Topological Indices of Some Dendrimers Structure.

A series of previously conducted experiments pertaining to various chemicals and drugs uncover a natural linkage between the molecular structures and the bio-medical and pharmacological characteristics. The forgotten topological index computed for the molecular structures of various chemical compounds and drugs has proven significant in medical and pharmaceutical fields by predicting biological features of new chemical compounds and drugs. A topological index can be considered as the transformation of chemical structure into a real number. Dendrimers are highly-branched star-shaped macromolecules with nanometer-scale dimensions. Dendrimers are defined by three components: a central core, an interior dendritic structure (the branches), and an exterior surface with functional surface groups. In this paper, we determine forgotten topological indices of poly(propyl) ether imine, porphyrin, and zinc-porphyrin dendrimers.