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Understanding the relationship between molecular structure and physicochemical properties is a central problem in mathematical chemistry and molecular informatics. Among the many topological descriptors used for this purpose, Zagreb indices play a significant role due to their proven relevance in quantitative structure-property relationship (QSPR) studies. Motivated by the need for structural insight into molecules modeled as trees, this work focuses on deriving lower bounds for the first and second Zagreb indices of trees with a fixed total domination number. By analyzing the structural properties of such trees, we establish new inequalities that highlight the interplay between domination parameters and molecular descriptors. To validate their practical relevance, we apply the derived bounds in a QSPR context, specifically examining their correlation with key physicochemical properties of alkanes. The statistical analysis reveals strong predictive capability, with near-to-unity correlation coefficients between the computed bounds and experimental data. These results demonstrate the potential of domination-theoretic methods in advancing predictive modeling in chemical graph theory.

This study introduces a novel approach to calculating graph entropies using topological indices, inspired by Shannon’s entropy concept. These entropies, as information-theoretic measures, are applied to evaluate the structural properties of chemical graphs. Graph theory is utilized to examine correlations between specific chemical properties and graph entropy measures. Within this framework, several physicochemical and quantum properties, including boiling point, enthalpy, molecular weight, and$$\\pi$$-electronic energy are analyzed. Certain new graph entropy measures, termed domination entropies, are introduced based on domination topological indices and computed for 29 benzenoid hydrocarbons. Additionally, a QSPR analysis is conducted to investigate the linear and multilinear relationships between these entropies and the physicochemical properties, as well as the$$\\pi$$-electronic energy of the hydrocarbons. The predictive accuracy of these new domination entropies is confirmed through various statistical tools.

This study presents a comprehensive analytical framework to examine and forecast the dynamics of India’s cashew production and cashew nut shell liquid (CNSL) exports. The analysis comprises two integrated components: a machine learning-based production forecasting system and a network topology analysis of India’s global CNSL trade relationships. For production forecasting, we develop a hybrid pipeline that integrates rolling Seasonal-Trend Decomposition using Loess (STL) with ensemble machine learning methods, specifically Random Forest and Gradient Boosting Machines, benchmarked against regularized linear models (Ridge and ElasticNet). To prevent data leakage, we implement a novel rolling STL decomposition approach that performs signal decomposition iteratively using only historical data available at each forecast origin. The methodology incorporates robust data preprocessing steps such as missing value imputation and normalization, along with temporal feature engineering involving lagged values, moving averages, rolling statistics, and year-on-year growth rates. To ensure reliable performance evaluation, we adopt an expanding window cross-validation strategy tailored for time series data across three temporal folds spanning 1999–2020. Among the models evaluated, Gradient Boosting demonstrates superior performance with an$$\\hbox {R}^{2}$$of 0.988 ($$\\pm 0.016$$), MAPE of 3.6% ($$\\pm 2.3\\%$$), and RMSE of 45.8 MT ($$\\pm 35.2$$), achieving 72% lower MAE compared to Ridge regression and outperforming Random Forest by 72% in mean absolute error. In the second component, we construct India’s global CNSL trade network spanning 1999–2020 and apply five centrality measures Degree, Closeness, Betweenness, Eigenvector, and PageRank to characterize its structure and identify key trading nodes. To further assess concentration and dependency, we introduce a novel Source-Importer Ratio metric, revealing pronounced disparities in trade influence, with differences of over 50-fold in degree centrality and 43-fold in PageRank across countries. The network analysis identifies India as the dominant hub with maximal degree centrality (1.0) and PageRank (0.461), while all importer countries exhibit uniformly low centrality scores (0.0196), confirming a star-like network topology with 52 nodes and 51 edges. By combining high-accuracy forecasting with network-driven diagnostics, this integrated approach provides a decision-support framework tailored to the needs of policymakers, exporters, and agri-business strategists. The study concludes with policy suggestions aimed at strengthening supply chain resilience, mitigating trade risks, and promoting export diversification. All code, data, and trained models are made publicly available to support reproducibility and adaptation to other perennial crop systems. Future work will extend the framework by integrating exogenous drivers such as climatic indicators and global price trends, and by updating the network analysis with post-2020 data to capture pandemic-induced structural changes in global trade patterns.

This article presents a short survey on 3-equitable and divisor 3-equitable labeling of graphs. For any graph G(V,E) and k > 0, assign vertex labels from {0,1,..., k − 1} such that when the edge labels induced by the absolute value of the difference of the vertex labels, the number of vertices labeled with i and the number of vertices labeled with j differ by at most one and the number of edges labeled with i and the number of edges labeled with j differ by at most one. We call a graph G with such an assignment of labels k -equitable. When k = 3, it becomes a 3-equitable labeling. In 2019, Sweta Srivastav et al. introduced the notion of divisor 3-equitable labeling of graphs. A bijection f: V(G) → {1, 2, ...,n} induces a function f':E(G) → {0,1,2} defined by for each edge e = xy, (i) f'(e) = 1 if f(x)|f(y) or f(y)|f(x), (ii) f'(e) = 2 if f(x)/f(y) = 2 or f(y)/f(x) = 2, and (iii) f'(e) = 0 otherwise such that | ef′(i)−ef′(j) |≤1 for all 0 ≤ i,j ≤ 2. A graph which admits a divisor 3-equitable labeling is called a divisor 3-equitable graph. This article stands divided into five sections. The first and fifth sections are reserved respectively for introduction and some important references. The second section deals with the 3-equitable labeling of graphs wherein some important known results have been recalled. The third section deals with the divisor 3-equitable labeling of graphs wherein a few known results have been outlined. In the fourth section we highlight certain conjectures and open problems in respect of the above mentioned labeling that still remain unsolved.

In this paper a new variant of divisor cordial labeling (DCL) named double divisor cordial labeling (DDCL) is in-troduced. A DDCL of a graph G ω having a node set V ω is a bijection g ω from V ω to 1,2,3,…, | V ω | such that each edge yz is given the label 1 if 2 g ω ( y )/ g ω ( z ) or 2 g ω ( z )/ g ω ( y ) and 0 otherwise, then the modulus of difference of edges labeled 0 and those labeled 1 do not exceed 1 i.e; | e g ω (0) — e g ω (1)| ≤ 1. If a graph permits a DDCL, then it is known as double divisor cordial graph (DDCG). In this paper we derive certain general results concerning DDCL and establish the same for some well known graphs.

A PCL of G is a bijective map g from V to 1, 2, 3, | V | in such a way that if an edge st is given label 1 if GCD ( g ( s ), g ( t )) = 1 & 0 otherwise, then the edges given 0 & 1 differ by at most 1 i.e; | e g (0) − e g (1)| ≤ 1. If a graph permits a PCL, then it is called a PCG. In this paper, we prove that lilly graph admits a PCL. Further, we have shown that lilly graph under some graph operations like switching of a vertex, duplication of a vertex, degree splitting graph and barycentric subdivision admits a PCL which may find its application in the development of artificial intelligence.

Over the past two decades, extensive research has elucidated the significant contributions of various nanomaterial such as metals, metal oxides, carbon nanotubes (single, double, and multi-wall), nanowires, and graphene in improving the tribological and thermal properties of AC & R systems used in both industrial and domestic settings. A recent research paper has specifically focused on the performance enhancement of AAC through the use of Nano-oxides, namely CuO, ZnO, and TiO2, employing mathematical modeling. This study investigates how dispersed Nano-oxides of CuO, ZnO, and TiO2, when added to a base of POE lubricant and HFC-R134a refrigerant, influence the performance of automobile air conditioning systems. The primary focus is on viscosity, heat transfer rate, and thermal conductivity of the working medium. The experimental results are compared with tested data, and further analysis is conducted using TK Solver 6.0 and Origin Lab software. The findings demonstrate that the incorporation of these Nano-oxides has a positive impact on thermal-physical properties (k-Thermal conductivity, ρ-viscosity, ρ-density and Cp-specific-heat) and heat transfer characteristics compared to systems without Nano-materials. Furthermore, there is a notable increase in Coefficient of Performance (COP) ranging from 23–29% with varying volume concentrations of Nano-oxides (0.5% to 2.5%) under atmospheric temperature conditions. Consequently, the combination of copper oxide, Zinc Oxide, and Titania nanoparticles with HFC-R134a as well as R1234ze (E) proves to be an effective approach for optimizing refrigerant properties and improving the performance of automobile air conditioning systems. Thus, Nano-oxides dispersion offer a promising solution for enhancing energy efficiency and reducing the reliance on conventional energy sources in thermal systems.

Automobile industries were ready to recycle the waste old parts as well as the damaged parts of the old vehicles as much as possible. This study mainly focused on the recycling of the waste and damaged aluminium frames of the automobile bodies. These aluminium-based frames only collected the metal matrix composite created by reinforcement of 3% silicon carbide (SiC) and 3% high carbon steel. The stir casting method is chosen to make the composites. Optimization is done by Taguchi ANOVA technique. Three input parameters such as stir speed, time of squeeze, and the temperature of the preheating were considered. The outputs such as compressive strength and porosity were experimentally measured with the combination of nine (L9) experimental trails. The measured experimental results were analyzed and optimized with the help of Taguchi technique with different plots for clear identification. The optimized parameters based on low porosity and high compressive strength were recommended for conclusion.

This article presents a short and concise survey on prime cordial and divisor cordial labeling of graphs. A prime cordial labeling of a graph G(V,E) is a bijective function f:V(G) → {1,2,...,|V|} such that if each edge xy is assigned the label 1 if gcd(f(x),f(y)) = 1 and 0 if gcd(f(x),f(y)) > 1, then the number of edges labeled with 0 and the number of edges labeled with 1 differ by at most 1. Further, a divisor cordial labeling of G is a bijection g: V(G) → {1,2,...,|V|} such that an edge st is assigned the label 1 if one g(s) or g(t) divides the other and 0 otherwise, then the number of edges labeled with 0 and the number of edges labelled with 1 differ by at most 1. We call G a divisor cordial graph if it admits a divisor cordial labeling. This article stands divided into five sections. The first and fifth sections are reserved respectively for introduction and some important references. The second section deals with the prime cordial labeling of certain classes of graphs wherein some important known results have been recalled. The third section deals with the divisor cordial labeling of graphs in which a few known results of high interest have been outlined. In the fourth section we highlight certain conjectures and open problems in respect of the above mentioned labelling that still remain unsolved.

Rapid population expansion, inadequate infrastructure, and a significant reliance on private automobiles are the main causes of traffic congestion in Indian cities, which causes delays and has a negative influence on the environment. Vehicle emissions pose a particularly serious problem for Chennai, a rapidly expanding metropolitan area with a population of around 10 million. Many metropolitan corridors are already functioning at saturation , with about 15% of families possessing vehicles and 50% owning motorbikes. The Hamiltonian circuit with a branch-and-bound approach is used in this study’s intelligent agent-based model for public transportation route optimization. When compared to the current linear routes, the optimal circular route between Poonamallee and Ambattur cuts average travel time by 18.6% and congestion by 21.4% out of the three possible options. A structured survey of 420 respondents along the Poonamallee High Road corridor was conducted to evaluate perceptions of transport choices and health impacts of vehicular pollution. According to the results, 31.8% of respondents named motor vehicles as the main cause of pollution, while 28.9% cited industrial activity. The frequency of respiratory problems was highest among younger individuals (25–35 years old) (52.7%), and women reported being more susceptible to asthma (45.7%) than men (24.5%). The choice for private vehicles was still driven by convenience, but notably, 42% of respondents with higher incomes thought that stronger regulations could lower pollution. All things considered, the findings show that route optimization can enhance urban mobility in Chennai’s transport system while lowering emissions and reducing hazards to public health.Article highlights Identified the most efficient route for urban commuters using congestion metrics and graph theory. Quantified the health impacts of vehicular congestion through statistical validation. Demonstrated that optimizing traffic routes can reduce exposure to air pollution and related illnesses.