Topological Indices Research Articles

Role of Solvents in Oriented Attachment of Ag Nanoparticles: Insights from Molecular Dynamics Simulations and Topological Analysis.

Although the solvation force is considered one of the key forces behind the oriented attachment (OA), the precise roles of solvents in this process remain incompletely elucidated. In this study, we examined the effect of solvent polarities (water, acetone, and chloroform) on the attachment of silver nanoparticles by calculating the free energy curves for the OA process. The observed magnitudes of the binding energies and approaching and dissociation energy barriers are commensurate with the respective solvent polarities. Consequently, OA is more likely to occur in acetone with an intermediate permittivity relative to that of water and chloroform. Additionally, we identified a topological descriptor, namely, the Euler characteristic, of the solvent network, especially the water network, between two approaching surfaces, which manifests a linear correlation with the observed free energy profiles. This descriptor holds promise as a quantitative tool for predicting interactions between nanoparticles in solvent environments featuring hydrogen bond networks.

On physical analysis of phthalocyanine iron (II) using topological descriptor and curve fitting models

A new area of applied chemistry called chemical graph theory uses combinatorial techniques to explain the complex interactions between atoms and bonds in chemical systems. This work investigates the use of edge partitions to decipher molecular connection patterns. The main goal is to use topological indices that capture important topological features to create a connection between the thermodynamic properties and structural characteristics of chemical molecules. We specifically examine the complex web of atoms and links that make up the Fe phthalocyanine chemical graph. Moreover, our study demonstrates a relationship between the calculated topological indices and the thermodynamic properties of Fe phthalocyanine (Phthalocyanine Iron (II)). This work offers insight into the thermodynamic consequences of molecule structures. It advances the subject of chemical graph theory, providing a useful perspective for future applications in catalysis and materials science.

New combined Inverse-QSAR and molecular docking method for scaffold-based drug discovery

Computer-aided drug discovery plays a vital role in developing novel medications for various diseases. The COVID-19 pandemic has heightened the need for innovative approaches to design lead compounds with the potential to become effective drugs. Specifically, designing promising inhibitors of the SARS-CoV-2 main protease (Mpro) is crucial, as it plays a key role in viral replication. Phytochemicals, primarily flavonoids and flavonols from medicinal plants, were screened. Fifty small molecules were selected for molecular docking analysis against SARS-CoV-2 Mpro (PDB ID: 6LU7). Binding energies and interactions were analyzed and compared to those of the anti-SARS-CoV-2 inhibitor Nirmatrelvir. Using these 50 structures as a training set, a QSAR model was built employing simple, reversible topological descriptors. An inverse-QSAR analysis was then performed on 2⁹ = 512 hydroxyl combinations at nine possible positions on the flavone and flavonol scaffold. The model predicted three novel, promising compounds exhibiting the most favorable binding energies (−8.5 kcal/mol) among the 512 possible hydroxyl combinations: 3,6,7,2′,4′-pentahydroxyflavone (PF9), 6,7,2′,4′-tetrahydroxyflavone (PF11), and 3,6,7,4′-tetrahydroxyflavone (PF15). Molecular dynamics (MD) simulations demonstrated the stability of the PF9/Mpro complex over 300 ns of simulation. These predicted structures, reported here for the first time, warrant synthesis and further evaluation of their biological activity through in vitro and in vivo studies.

Correlations between meaning in life and nature connectedness: German-language validation of two topic-related measures and practical implications

Abstract Meaning in life and nature connectedness are indicators of a healthy life and correlate with health and well-being. We conducted a validation study of German versions of the Meaning in Life Questionnaire (Steger et al. 2006) and Nature Connection Index (Richardson et al. 2019) and assessed mindfulness as a trait and personality (big five personality traits) among participating students (n = 353). Results indicated a significant positive correlation between nature connectedness and presence of meaning in life. Presence of meaning correlated significantly with less neuroticism, more openness to new experiences, greater conscientiousness, and moderately with the two mindfulness subscales, ‘acceptance’ and ‘presence’. Search for meaning was associated with more neuroticism and less acceptance. A higher nature-connectedness score correlated with more presence and acceptance (mindfulness), greater openness, and less neuroticism (personality traits). Furthermore, we introduce a nature-assisted model of meaning fulfilment that can be applied in healthcare practices, counselling, and (psycho-) therapeutic treatment. Our results contribute to growing evidence on the preventive and curative effects of nature connectedness and meaning in life and their role as health-related resources. Nature connectedness and meaning in life are effective resources considering various aspects related to (global) crises such as climate change and the corona pandemic.

Exploring Entropy Measures with Topological Indices on Subdivided Cage Networks via Linear Regression Analysis

ABSTRACT In this study, we investigate entropy measurements for subdivided cage networks based on topological indices. We specifically calculate different entropy, redefining Zagreb entropy, HM ( G ) , M 1 ( G ) , M 2 ( G ) entropy, atom bond connection entropy, and Randic entropy. We examine the graphical behavior of various entropy measures using the line fit approach. The results highlight patterns in the distribution of entropy values and interactions between them, which shed light on the intricate connectivity and structural properties of segmented cage networks. This work improves our understanding of cage network dynamics and provides a visual framework for interpreting their behavior.

Topological photonic band gaps in honeycomb atomic arrays

lattice of two-level atoms coupled by the in-plane electromagnetic field may exhibit band gaps that can be opened either by applying an external magnetic field or by breaking the symmetry between the two triangular sublattices of which the honeycomb one is a superposition. We establish the conditions of band gap opening, compute the width of the gap, and characterize its topological property by a topological index (Chern number). The topological nature of the band gap leads to inversion of the population imbalance between the two triangular sublattices for modes with frequencies near band edges. It also prohibits a transition to the trivial limit of infinitely spaced, noninteracting atoms without closing the spectral gap. Surrounding the lattice by a Fabry-Pérot cavity with small intermirror spacing d < \pi/k_0d<π/k0, where k_0k0 is the free-space wave number at the atomic resonance frequency, renders the system Hermitian by suppressing the leakage of energy out of the atomic plane without modifying its topological properties. In contrast, a larger dd allows for propagating optical modes that are built up due to reflections at the cavity mirrors and have frequencies inside the band gap of the free-standing lattice, thus closing the latter.

On curve fitting between topological indices and Gibb’s energy for semiconducting carbon nitrides network

Quantitative structure relationships linked to a chemical structure that shed light on its properties and chemical reactions are called topological indices. This structure is upset by the addition of silicon (Si) doping, which changes the electrical and optical characteristics. In this article, we examine the connection between a chemical structure’s Gibbs energy (GE) and K-Banhatti indices. In this article, we compute the K-Banhatti indices and then show the correlation between the indices and Gibb’s energy of the molecule using curve fitting. Through the curve fitting, we see that there is a strong correlation between indices and Gibb’s energy of a molecule. We use the polynomial curve fitting approach to see the correlation between indices and Gibb’s energy.

Algorithms for Distance-based Topological Indices for Zero Divisor Graphs of Commutative Rings with Primes

Mathematical solutions are sometimes complex to solve mathematically. Algorithms can provide the solution to these problems. Our article introduced algorithms to compute distance-based topological indices for zero divisor graphs containing finite rings as Zp1p2 × Zq. and Zp2 × Zq, having primes p1, p2, and q. Algorithm results can be reused in standing physical structures, solving computer network problems, and designing mechanics.

Group Theoretic Approach towards the Balaban Index of Catacondensed Benzenoid Systems and Linear Chain of Anthracene

In this work, we present the analytical closed forms of the Balaban index for anthracene and catacondensed benzenoid systems using group theoretic techniques. The Balaban index is a distance-based topological index that provides valuable information about the properties of chemical structures. We emphasize the importance of determining analytical closed forms of the Balaban index for catacondensed benzenoid systems and linear chains of anthracene, as it enables a deeper understanding of these systems and their behavior. Our analysis utilizes the group action of the automorphism group of these chains on the set of vertices, which refer to the points where the chains intersect. In future work, we plan to determine the Balaban index of other polymeric linear chains using group theoretic techniques and extend the applications of this index to other fields, such as materials science and biology. It is clear that the Balaban index remains a valuable tool in theoretical and computational chemistry, and its applications are constantly evolving.

Changes in urban green space configuration and connectivity using spatial graph-based metrics in Ardabil developing city, Iran.

Urban planning is essential for managing the diverse impacts of urban green spaces, such as public access, stormwater control, urban life quality, and landscape aesthetics, promoting sustainable urban development and urban residents' well-being by integrating green space considerations into city planning. The aim of this study is to use graph-based metrics to calculate the connectivity of UGS across the main municipal zones of Ardabil city over consecutive periods under different population growth rates. Another objective of this study is to compare the connectivity values of UGS in the four municipal zones and to evaluate changes in the connectivity indices at various distance thresholds of UGS patches. After identifying UGS in different periods, the changes in graph-based connectivity indices at various distance thresholds of UGS patches were analyzed. Additionally, the changes in connectivity indices over different periods and across various municipal zones were compared and analyzed. The findings reveal that UGS areas were larger in the past but have recently had smaller patch sizes. Connectivity between UGS nodes (dNL) decreased at various distances over the study years, showing a declining trend in different connectivity indices. UGS connectivity decreased in municipal zones 1, 2, and 3 but increased in recent years after a decline until 2012 across all four zones of Ardabil city. Zone 4 had the highest UGS connectivity due to newly developed urban areas and well-allocated UGSs. Integrating the ecological impacts of UGS connectivity in urban development and design will enhance trade-offs between conservation, public health, and social equity. New urban areas should allocate sufficient land for UGS and parks, ensuring accessibility to support health and leisure through municipal planning. The study highlights the need for sustainable urban development policies that prioritize the allocation and maintenance of UGSs.

Entropy measures of dendrimers using degree based indices

Topological indices play a crucial role as molecular descriptors in QSAR/QSPR research. Graph entropy measurements are of great importance in various fields like chemistry, discrete mathematics, and biology. Information-theoretic values derived from topological indices, influenced by Shannon’s entropy, are used to analyze the structural characteristics of chemical graphs and complex networks. We discuss the analysis of graph entropies obtained from a new information function. It is equivalent to both the total number of edges and the various degrees of vertices. The information function is also employed to compute the entropies of the system and build a connection between connectivity indices and degrees. This study examines the chemical graphs of Carboxylate-terminated Zinc Phthalocyanine (CtZP) and Nanostar (NS), using the function to connect degree-based topological indices like First Zegrab index, Second Zagreb index, Hyper Zagreb index, Forgotten index, First Redefined Zagreb index, The Second Redefined Zagreb index, The Third Redefined Zagreb index, and Somber index, to calculate the entropies of these structures.

Computing Degree-Based Topological Descriptors of Certain Tessellations of Kekulenes Using M-Polynomial and Neighborhood M-Polynomial

Topological indices are well-known molecular descriptors that may be applied to any graph and to model specific molecular structures, utilized for property correlation in quantitative structure activity and property relationship (QSAR and QSPR) analyses. Strong methods for machine learning information and thermodynamic simulations of massive networks and nanomaterials can be facilitated by using topological indices. Kekulenes are a novel type of cycloarenes, arranged in doughnut-shaped cyclic benzene rings with riveting superaromaticity and other significant properties. The main aim of this paper is to ascertain the notable degree and the neighborhood degree sum-based indices through M-polynomials and neighborhood M-polynomials of certain types of tessellations of kekulenes. Then, a graphical comparison of the resulting indices is also performed.

On Topological Indices of Fuzzy Random Graph

On Topological Indices of Fuzzy Random Graph

Predicting graph energy and entropy analysis of pent-heptagonal nanomaterials: Insights from regression models using generalized reverse degree-sum topological indices

Nanostructures have sparked notable interest in materials science due to their diverse applications, especially carbon nanosheets with pentagonal–heptagonal variations have emerged as subjects of intense scientific investigation. These nanostructures show great potential in a wide range of fields, including energy storage, optoelectronics, catalysis, and bioelectronics, thereby making substantial contributions to nanotechnology and material science. Topological indices hold a pivotal position in the domain of mathematical and computational chemistry providing numerical information about molecular structures. This information is instrumental in establishing predictive relationships with chemical and physical properties, finding applications across various fields such as drug development and materials science. This paper introduces a novel generalized version of reverse degree-sum based topological indices that effectively shaping the degree sequence of nanomaterials to fit the physical and chemical properties of dataset, differentiating it from conventional fixed-degree methods. Consequently, we explore entropy-based methodologies to compare the structural complexities of pent-heptagonal nanosheets. Furthermore, our study predicts the graph energies of these nanosheets via linear regression equations, comparing them with energy values predicted by the McClelland equation.

Hyper-Zagreb index in fuzzy environment and its application

The Zagreb indices (ZIs) are important graph invariants that are used extensively in many different fields in mathematics and chemistry, such as network theory, spectral graph theory, fuzzy graph theory (FGT) and molecular chemistry, etc. The hyper-ZI is introduced especially for fuzzy graphs (FGs) in this study. The study computes this index's bounds for a variety of FG types, including paths, cycles, stars, complete FGs and partial fuzzy subgraphs. It is shown that isomorphic FGs produce the same values for this index. Moreover, interesting connections are established between the hyper-ZI and the second ZI for FGs. Moreover, bounds on this index are found for the following operations: direct product, Cartesian product, composition, join, union, strong product and semi-strong product of two FGs. In the end, the effectiveness of this index is compared with three other topological indices: hyper-ZI for crisp graphs, first ZI for FGs and F-index for FGs, in an analysis of the crime “Murder” in India. While the hyper-ZI for FGs, first ZI for FGs and F-index for FGs yield similar outcomes, the hyper-ZI for FGs demonstrates superior realism in detecting crimes in India compared to its crisp graph counterpart.

Mathematical modeling for prediction of physicochemical characteristics of cardiovascular drugs via modified reverse degree topological indices.

Global health concerns persist due to the multifaceted nature of heart diseases, which include lifestyle choices, genetic predispositions, and emerging post-COVID complications like myocarditis and pericarditis. This broadens the spectrum of cardiovascular ailments to encompass conditions such as coronary artery disease, heart failure, arrhythmias, and valvular disorders. Timely interventions, including lifestyle modifications and regular medications such as antiplatelets, beta-blockers, angiotensin-converting enzyme inhibitors, antiarrhythmics, and vasodilators, are pivotal in managing these conditions. In drug development, topological indices play a critical role, offering cost-effective computational and predictive tools. This study explores modified reverse degree topological indices, highlighting their adjustable parameters that actively shape the degree sequences of molecular drugs. This feature makes the approach suitable for datasets with unique physicochemical properties, distinguishing it from traditional methods that rely on fixed degree approaches. In our investigation, we examine a dataset of 30 drug compounds, including sotagliflozin, dapagliflozin, dobutamine, etc., which are used in the treatment of cardiovascular diseases. Through the structural analysis, we utilize modified reverse degree indices to develop quantitative structure-property relationship (QSPR) models, aiming to unveil essential understandings of their characteristics for drug development. Furthermore, we compare our QSPR models against the degree-based models, clearly demonstrating the superior effectiveness inherent in our proposed method.

Switching to a 100% remote follow-up of implantable cardiac electronic devices: Organizational model and results of a single center experience.

During the SARS-CoV-2 COVID-19 pandemic, the global health system needed to review important processes involved in daily routines such as outpatient activities within the hospital, including follow-up visits of implantable cardiac electronic devices (CIEDs) carried out in office. The aim of this study is to describe our 3.5 years of real-world experience of a full remote CIED follow-up, evaluate the success rate of remote transmissions, and verify the adopted organizational model. From April 2020 to November 2023, all patients with an activated and well-functioning remote monitoring (RM) system and automatic algorithms, like autocapture and autosensing, underwent exclusive RM follow-up. Unscheduled in-office visits were only prompted by remote yellow or red alerts. Patients were divided into two groups, based on available technology: Manual Transmission System (MTS) and Automatic Transmission System (ATS). The ATS group, in addition to ensuring a daily transmission of any yellow or red alerts, was checked at least every 15 days to ensure a valid connection. An automatic transmission was scheduled once a year, irrespective of alerts occurred. The MTS group provided a manual transmission every 6 months. One thousand nine hundred thirty-seven consecutive patients were included in the study. By the end of November 2023, a total of 1409 patients (1192 in the ATS and 217 in the MTS group) were still actively followed by our remote clinic (384 expired, 137 dismissed, 7 transferred). The overall success rate of transmissions with the adopted organizational model was 96.6% in the ATS group (connection index) and 87% in the MTS group. Conventional in-hospital follow-up visits decreased by 44%. Total clinic working time, resulting from the sum of the time spent during in-hospital and remote follow-up, after an initial increase, was progressively reduced to the actual -25%. Mortality rate for any cause was 7.5% per year in remote follow-up patients and 8.3% (p=NS) in in-office patients. In the ATS group, no device malfunctions were notified to our remote clinic, before we had already realized it through appropriate alerts. The available technology makes moving to a 100% remote clinic possible, without overwhelming clinic workflow, safely. Adopting an appropriate organizational model, it is possible to maintain high transmission success rates. The automatic transmissions allow a more frequent control of patients with CIED.

Explaining recovery from coma with multimodal neuroimaging

The aim of this prospective, observational cohort study was to investigate and assess diverse neuroimaging biomarkers to predict patients’ neurological recovery after coma. 32 patients (18–76 years, M = 44.8, SD = 17.7) with disorders of consciousness participated in the study. Multimodal neuroimaging data acquired during the patient’s hospitalization were used to derive cortical glucose metabolism (18F-fluorodeoxyglucose positron emission tomography/computed tomography), and structural (diffusion-weighted imaging) and functional connectivity (resting-state functional MRI) indices. The recovery outcome was defined as a continuous composite score constructed from a multivariate neurobehavioral recovery assessment administered upon the discharge from the hospital. Fractional anisotropy-based white matter integrity in the anterior forebrain mesocircuit (r = 0.72, p < .001, 95% CI: 0.87, 0.45), and the functional connectivity between the antagonistic default mode and dorsal attention resting-state networks (r = − 0.74, p < 0.001, 95% CI: − 0.46, − 0.88) strongly correlated with the recovery outcome. The association between the posterior glucose metabolism and the recovery outcome was moderate (r = 0.38, p = 0.040, 95% CI: 0.66, 0.02). Structural (adjusted R2 = 0.84, p = 0.003) or functional connectivity biomarker (adjusted R2 = 0.85, p = 0.001), but not their combination, significantly improved the model fit to predict the recovery compared solely to bedside neurobehavioral evaluation (adjusted R2 = 0.75). The present study elucidates an important role of specific MRI-derived structural and functional connectivity biomarkers in diagnosis and prognosis of recovery after coma and has implications for clinical care of patients with severe brain injury.

Geomorphic assessment of sediment storage potential and mobilisation on the hillslopes of a mountain catchment: An example from Pranmati catchment, NW Himalaya

Sediment budgeting within a landscape is useful in understanding landscape evolution, and hazard prediction and assessment. It has been observed that only a fraction of the total volume of sediment produced within the system gets exported, implying that a part of the total volume of sediment is stored within the system. This sediment mass gets arrested and stored in compartments within the system and is mobilised during extreme stochastic events. These sediment storage compartments are poorly connected with the channel network and hence, do not supply sediment at steady rates. We have evaluated sediment connectivity and conducted field validation within a 93 km2 mountainous river basin (Pranmati catchment) in the NW Himalayas. This assessment relies on the Index of Connectivity (IC), computed through two methods: one employing the original framework and the C-factor from RUSLE, and the other utilizing a multiple flowpath model that incorporates Manning's roughness coefficient. We developed a storage potential index (SPI) by modifying the basic framework of index of connectivity; SPI indicates the potential of a point on the hillslope to arrest sediment flux and store it. Based on the difference of normalised IC and SPI, we have developed a sediment evacuation susceptibility index (ESIS) that indicates the susceptibility of various parts of the hillslope to get evacuated. Using ESIS, a sediment evacuation susceptibility zonation map was prepared that delineates areas on the basis of their stability.Our study indicates that sediment flux gets arrested at the (1) junction of land use and land cover units that have contrasting sediment transporting capacity, (2) grassland/barren land pockets surrounded by forests, (3) croplands, and (4) landslide debris deposits. The parts of the hillslope in the vicinity of the channel network and areas around steep surfaces are highly susceptible to sediment evacuation. Gentle sloped surfaces away from the channel network are relatively stable. Landslide debris are highly stable units of sediment storage.

Topological Characterization for Triangular, RegularTriangular Oxides and Silicates Networks

Chemical graph theory can be studied with the aid of mathematical tools called m-polynomials. M-Polynomials offer a potent tool for computing different topological indices associated with vertex degrees and analyzing degree-based structural information in graphs. By counting specific substructure types within them, they are able to encode information about the structure of molecules or networks. In this article, we have developed M-Polynomials with the help of different topological invariants such as first Zagreb (M1(β)), second Zagreb (M2(β)), second modified Zagreb (Mm2(β)), inverse sum (I(β)), harmonic index (H(β)) and Randic index (Rα0(β)) for the molecular structures of Triangular oxide TOX(r), Regular triangular oxide RTOX(r), Triangularsilicate TSL(r) &amp; Regular triangular silicate RTSL(r) networks to introduce new closed formulas to get better understanding the applications of M-Polynomials and topological indices in mathematical chemistry especially in the field of QSAR and QSPR study with the help of some software like MATLAB. We have also discussed the graphical behaviors of the above-mentioned structures.