Ensuring digital image security is critical in today’s edge computing and networked communication environments. Chaotic systems offer powerful tools for lightweight, real-time encryption, but often suffer from limited chaotic ranges and weak key sensitivity. This paper introduces a robust nonlinear RN chaotic system, combining two chaotic maps to enhance unpredictability and expand the chaotic interval. A fast image encryption scheme is then developed by integrating this system with elliptic-curve Diffie–Hellman (ECDH) key exchange, hierarchical key derivation (HKDF), and dynamic chaotic S-box generation. The scheme ensures plaintext-independent key generation, authentication via ECDSA, and integrity through HMAC-SHA256, thereby preventing man-in-the-middle attacks and key leakage. Using the same set of security keys, this algorithm can produce a completely different encrypted image each time it is applied to the same original image. The proposed technique consistently achieves near-ideal entropy levels (~ 7.999), high NPCR (> 99.61%), and UACI above 32%, image complexity (with a keyspace equal to 10²⁵⁶), and resistance to security attacks, demonstrating outstanding sensitivity and randomness. The low PSNR values and limited correlation of the encrypted images further show strong resilience to statistical and differential assaults. The proposed approach outperforms existing methods in terms of computational reliability, encryption strength, and unpredictability. This work provides a dependable, portable, and efficient solution for secure image transfer in surveillance and multimedia applications.

Amino acids, as the fundamental constituents of proteins and enzymes, play a vital role in various biological processes. Amino acids such as histidine, cysteine, and methionine are known to coordinate with metal ions in proteins and enzymes, playing critical roles in their structure and function. In metalloproteins, metal ions are often coordinated by specific amino acid residues, contributing to the protein’s stability and catalytic activity. Investigating the structural properties of amino acids is paramount to understanding the intricacies of protein function and interactions. The molecular structure of amino acid structures are examined using topological indices that are based on both distance and degree. These indices capture unique structural features of amino acids in their molecular graphs. We have developed linear, quadratic, and logarithmic regression models to estimate the five physical/chemical properties of twenty-two amino acids molecules. The findings reveal novel insights into the structural determinants of amino acid properties and present efficient predictive models for various attributes. This research contributes towards better understanding amino acid structures and offers practical applications in bioinformatics, drug design, and structural biology, enhancing the ability to manipulate and comprehend the molecular world.

Objectives: In the field of graph theory, an intuitionistic fuzzy set becomes a useful tool to handle problems related to uncertainty and impreciseness. We introduced the interval-valued intuitionistic fuzzy line graphs (IVIFLG) and explored the results related to IVIFLG. Result: Some propositions and theorems related to IVIFLG are proposed and proved, which are originated from intuitionistic fuzzy graphs (IVIG). Furthermore, Isomorphism between two IVIFLGs toward their IVIFGs was determined and verified.

The notion of Bipolarity based on positive and negative outcomes. It is well known that bipolar models give more precision, flexibility, and compatibility to the system as compared to the classical models and fuzzy models. A bipolar fuzzy graph(BFG) provides more flexibility while modeling human thinking as compared with a fuzzy graph, and an interval valued bipolar fuzzy graph(IVBFG) has numerous applications where the real-life problem are time dependent and there is a network structure complexity. The aim of this paper is to introduce an interval-valued bipolar line fuzzy graph(IVBFLG). In this paper, we have proposed the notion of an IVBFLG and some of its characterizations. Also, some propositions and theorems related to an IVIFLGs are developed and proved. Furthermore, isomorphism between two IVIFLGs toward their IVIFGs was determined and verified. As a result, we derive a necessary and sufficient condition for an IVBFG to be isomorphic to its corresponding IVBFLG and some remarkable properties like degree, size, order, regularity, strength, and completeness of an IVBFLGs have been investigated, and the proposed concepts are illustrated with the examples.

Quantitative structure-property relationship (QSPR) and Quantitative structure-activity relationship QSAR modeling are constructed on the principle, which describes that biological activity and physicochemical properties of a chemical compound can be deduced from its chemical structure. These relationships are commonly developed from graph invariants that can be computed from the molecular graphs of chemical compounds. Coronary artery disease occurs when the coronary arteries become narrowed or blocked, which can restrict the flow of oxygen-rich blood to the heart. Coronary artery disease is the leading cause of disability-adjusted life years lost and death worldwide. This study advances QSPR modeling by using eccentricity-based graphical invariants, specifically designed to enhance the predictive accuracy for physicochemical properties of drugs used to treat coronary artery disease, including atorvastatin, simvastatin, rosuvastatin, aspirin, clopidogrel, metoprolol, atenolol, enalapril, lisinopril, amlodipine, diltiazem, nitroglycerin, isosorbide dinitrate, ranolazine, gemfibrozil, and fenofibrate. We used the cubic, logarithmic, quadratic, and linear models to explore the structure-property relationship of drugs for coronary artery disease. We designed the models on the basis of the adjusted r-squared values, assuming the eccentricity-based invariants as independent variables, while the physico-chemical properties of sixteen drugs as dependent variables. The dependent variables include boiling point, enthalpy of vaporization, heavy atom count, molar volume, polarizability, complexity, molecular weight, and molar refractivity. The statistical analysis indicates that the most suitable structure-property models are nonlinear. The findings show that the eccentric Albertson index and the eccentric geometric arithmetic index attain superior predictive performance compared to other indices. The analysis shows that cubic regression is the optimal choice for predicting enthalpy of vaporization, molar refractivity, polarizability, and complexity. In contrast, quadratic regression is the best option for predicting molecular weight, while a linear model is most effective for assessing heavy atom count. Additionally, logarithmic regression is the most suitable choice for boiling point and molar volume. To validate the robustness of our regression models, we used them to assess the properties of five additional coronary artery disease drugs that were not part of the original dataset. The experimental values were compared with forecasted data, revealing a strong correlation between them. This demonstrates the reliability of our regression models in assessing these vital physicochemical parameters.

Parkinson’s disease is a progressive neurological disorder characterized by the degeneration of the nervous system, leading to impaired motor and non-motor functions. Early symptoms include tremors, rigidity, and bradykinesia, with progressive deterioration over time. This study employs a multi-criteria decision-making approach, integrating Fuzzy TOPSIS and Quantitative Structure–Property Relationship (QSPR) analysis, to evaluate and rank 17 Parkinson’s disease medications based on their physicochemical properties. Molecular structures were encoded as adjacency matrices using MATLAB 2017, and six Sombor index variants—computed via a custom Maple 2020 algorithm—served as topological descriptors for QSPR modeling. Eight critical physicochemical properties were analyzed: polarizability (P), boiling point (BP), surface tension (ST), polar surface area (PSA), flash point (FP), molar refractivity (MR), enthalpy of vaporization (EV), and molar volume (MV). The Fuzzy TOPSIS ranking revealed bromocriptine as the top-performing drug for boiling point (BP), while comparative rankings across all properties are tabulated for clinical reference. Validation metrics, including coefficient of determination, mean squared error , and mean absolute error, confirmed model robustness. Notably, surface tension (ST) and polar surface area (PSA) showed weaker correlations (R² < 0.5, p > 0.05), highlighting limitations in their predictability via Sombor indices. This work demonstrates the utility of combining chemical graph theory, QSPR modeling, and Fuzzy TOPSIS for rational drug evaluation in neurodegenerative disorders. The methodology offers a framework for prioritizing therapeutics based on physicochemical profiles, with implications for optimizing Parkinson’s disease management.