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ORDER SUM SIGNED GRAPH OF A GROUP
The order sum graph associated with the group G, denoted by ?os, is a graph with vertex set consisting of elements of G and two vertices say a,b ? ?os are adjacent if o(a) + o(b) > o(G), where o(?) denotes the order of a group or an element of a group. In this paper, we introduce a signed graph called order sum signed graph where the underlying graph is a complete graph of order n and the edges receive positive and negative signs based on the order sum graph. We characterise the balanced negated order sum signed graphs. We also characterise the positive and negative homogeneous order sum signed graphs. Further, we study the properties such as clusterability, sign-compatibility, consistency and switching of signed graphs. Further, we obtain the adjacency spectra, Laplacian spectra and signless Laplacian spectra of the order sum signed graphs associated with cyclic groups. 2025, University of Guilan. All rights reserved. -
ON THE INDICES OF CERTAIN GRAPH PRODUCTS
Molecular descriptors are numerical graph invariants that are used to study the chemical structure of molecules. In this paper, we determine the upper bound of the Sombor index based on four operations involving the subdivision graph, semi-total point graph, semi-total line graph, and total graph related to the lexicographic and tensor product. The exact expressions of the first reformulated Zagreb index and the second hyper-Zagreb index of the tensor product are formulated on the basis of the four significant graphs. Further, the descriptors for certain standard graphs are obtained and the graphical comparison for the first reformulated Zagreb index has also been illustrated to understand the result better. 2025 University of Isfahan -
An Efficient Approach for Gene Selection through Parallel Bio-Inspired Algorithms and Shapley Value Analysis
The fast development of microarray technology has significantly assisted in the use of gene expression analysis to forecast cancer subtypes. Analyzing high-dimensional microarray data is still challenging, as existing hybrid methods cannot find highly discriminative genes. This study aims to use Shapley value analysis and hybrid bio-inspired algorithms to develop a scalable, parallel gene selection technique to increase computing efficiency and classification accuracy in high-dimensional microarray data. This study used hybrid feature selection approaches inspired by bio-organisms to create a scalable parallel gene selection system. The dataset size is initially enlarged by Adaptive Synthetic Sampling (ADASYN). They use the Recursive Feature Elimination (RFE) approach to extract features and determine their Shapley values. In addition, the Whale Optimization Algorithm (WOA) works to determine which genes are most important. After that, Machine Learning (ML) techniques assist in classifying the chosen characteristics. According to the experiment results, the suggested strategy surpasses standard gene selection techniques with the same datasets, employing improved classification accuracy and reducing computing time. K-NN achieved an accuracy of 85.44%, while LR showed improved results with an accuracy of 91.72%. RF further increased accuracy to 94.69%. SVM demonstrated exceptional performance, reaching an accuracy of 97.63%. Ultimately, XGBoost excelled among all models with the highest accuracy of 98.49%, highlighting its robust ability to classify SRBCT samples effectively based on gene expression data. 2025, Ayandegan Institute of Higher Education. All rights reserved. -
Enhancing Experimental Efficiency in Uncertain Data: A Comparative Analysis of Neutrosophic and Classical Latin Square Designs
This research investigates the relative efficiency between Neutrosophic Latin Square Design (NLSD) and Classical Latin Square Design (CLSD), with a particular focus on their use in situations where data is uncertain and ambiguous. Although CLSD is a classic experiment designed for systematic error control, its utility is limited in fields like agriculture and behavioral sciences due to its performance bottleneck regarding data imprecision. The NLSD can relatively easily be extended to incorporate neutrosophic logic to address these challenges, making it a more powerful tool for modeling uncertainty. In this paper, a systematic efficiency evaluation of NLSD against CLSD is performed for inconsistent data. It is found that the NLSD enables significant improvements in experimental efficiency while providing clearer inferences regarding treatment effects and supporting more reliable conclusions. Despite these limitations, these benefits establish NLSD as a promising candidate for overcoming environmental uncertainties, and these observations hold significant potential to further the advancement of experimental designs. The results demonstrate that NLSD conveys a 55 % chance to enhance efficiency relative to LSD, which is especially important in processes that must attain maximum resource utilization and high experimental efficiency. 2025, Ayandegan Institute of Higher Education. All rights reserved. -
Integrating Hesitant Fuzzy Sets with Machine Learning for Enhanced Healthcare Predictive Analytics
This study examines how Hesitant Fuzzy Sets (HFS) and Machine Learning (ML) might improve healthcare predictive analytics. HFS, which accommodates uncertainty and hesitation in decision-making, is used to improve healthcare projections. Predictive analytics methods struggle with data ambiguity and imprecision, resulting in poor decision-making. Traditional ML algorithms may not be able to collect hesitant information, resulting in less accurate patient outcomes and treatment recommendations. The Integrating Hesitant Fuzzy Sets with ML (IHFS-ML) framework overcomes these issues by integrating HFS flexibility with advanced ML approaches. This connection allows the representation of ambiguous patient data for better healthcare analytics. Data pre-processing in the IHFS-ML framework improves healthcare analytics prediction. These methods transform uncertain fuzzy data into an ML-friendly format. Disease prediction, patient risk assessment, and therapeutic effectiveness analysis are recommended. The approach aims to improve healthcare decision-making and deliver new insights by merging hesitant and ambiguous information. IHFS-ML uses HFS to characterize imprecise and confusing patient data. These HFS are combined with powerful ML classifiers like Random Forest (RF) and Logistic Regression. The IHFS-ML system outperforms current prediction accuracy and reliability methods, suggesting it might transform healthcare analytics. HFS improves ML model interpretability, improving patient outcomes and healthcare decisions. Compared to other methods, the IHFS-ML model improves prediction analysis reliability by 99.7%, scalability by 97.6%, data pre-processing efficiency by 97.1%, interpretability by 98.9%, and accuracy by 97.8%. 2025, Research Expansion Alliance (REA). All rights reserved. -
Adaptive Fuzzy Heuristic Algorithm for Dynamic Data Mining in IoT Integrated Big Data Environments
The explosion of Internet of Things (IoT) devices has created enormous amounts of real-time data, requiring sophisticated Data Mining Methods (DMT) that can rapidly extract valuable insights. Managing the computational complexity of processing high data volumes, integrating various IoT data formats, and ensuring that the system can scale are among the most significant issues. Fuzzy Dynamic Adaptive Classifier Optimization Analysis (FDACOA) is a method that has been suggested as an approach to the difficulties caused by changes in data patterns, processing in real-time, and data heterogeneity. By incorporating Adaptive Fuzzy Logic (AFL) and heuristic optimization, FDACOA enhances data classification accuracy and efficiency while simultaneously assuring that the algorithm can adapt to changes in data streams. This adaptability is crucial in IoT applications, where data fluctuation might affect analysis quality. FDACOA uses dynamic adaptation to alter classifier parameters based on real-time feedback to improve prediction accuracy and reduce computing costs. An optimization layer fine-tunes fuzzy rules and membership functions to optimize performance across data situations. Simulation analyses proved the algorithm's capacity to classify with high accuracy and low computational cost. Smart healthcare, predictive maintenance in industrial IoT, and intelligent transportation systems use FDACOA for real-time decision-making and data-driven insights. FDACOA is a viable approach for dynamic data mining in IoT-enabled big data contexts because of its faster, more accurate, and more adaptable simulation results. 2025, Research Expansion Alliance (REA). All rights reserved. -
Influence of Cooking and Fermentation on Nutrient and Anti-nutrient Profiles of Millet and Rice; [????? ??? ? ????? ?? ?????????? ???? ???? ? ?????? ?? ?????? ? ??? ?]
This study investigates how the traditional processing methods, such as cooking and fermentation, affect the nutritional, anti-nutritional, and mineral composition of the six edible grains, including the three rice varieties (Oryza sativa: Matta, Boiled and Brown rice) and the three millets (foxtail, jowar and pearl millet). The grains were analyzed in their raw, cooked, and fermented forms. The carbohydrates and the protein content were determined along with the anti-nutritional compounds such as the flavonoids, oxalates, phenolics, phytates and the tannins. The mineral concentrations of calcium, potassium, iron, magnesium, manganese, and zinc were determined using Atomic Absorption Spectroscopy. The results showed that cooking significantly reduced carbohydrate content by 85-90% across all grains, while fermentation caused an even greater reduction of up to 95%. Protein levels were grain-specific, and fermentation generally enhanced the protein concentration by 20 50%. Flavonoid content was reduced by 70-90% while phytates, and oxalates were reduced substantially by 60 90% through both treatments due to leaching and thermal degradation, while the phenolic content increased by 25-40%, particularly in the foxtail millet. The tannin levels decreased with cooking by 40-60%, but they increased after the fermentation, likely due to the enzymatic release of the bound compounds. Mineral concentrations were consistently declined in the cooking and fermented forms, yet fermentation improved bioavailability by reducing the anti-nutrients. Overall, the cooking was more effective in lowering the anti nutritional factors, whereas the fermentation enhanced the protein and improved the accessibility of the essential minerals such as iron and zinc. These findings emphasizes the importance of the traditional household processing methods in enhancing the nutritional quality of rice and millet-based diets, particularly in the regions dependent on cereal staples. 2025, Ferdowsi University of Mashhad. All rights reserved. -
Attentional Deep Learning with Inverse Transform Sampling for Robust Respiratory Sound Classification
The necessity for efficient breathing sound classification systems originates from respiratory diseases, which impair oxygen-carbon dioxide exchange and impact lung function. Feature extraction and pattern categorization are general components of such systems. Because of their effectiveness with big datasets, deep neural networks have acquired popularity recently in the category of breathing sounds. Enhancing medical care requires cooperation amongst researchers, medical professionals, and patients. An attentional deep learning model with inverse transform sampling is presented in this study to classify respiratory diseases from audio data. Robust models were developed to classify and detect respiratory elements using the Respiratory Sound dataset. The primary objectives include effectively determining lung sounds and determining respiratory illnesses. The architectures of CNN, VGG16, and ResNet50 were developed to extract features and categorize data. Also, the pre-trained models ResNet50 and VGG16 identify critical characteristics in spectrum pictures more accurately. Inverse transfer sampling is used to rectify class imbalance in respiratory datasets. The models achieved 98% accuracy with the CNN model, 83% accuracy with VGG16, and 95% accuracy with ResNet50. Moreover, LSTM and CRNN models offer more information on how respiratory illnesses are classified. 2026, Hemanth K S, Harisha Naik T, N Kartik, N Nanda kumar, S Senthilkumar and Ramya R. -
Examining the Components of Organizational Attractiveness: An Employee Perspective
This study examines the key components influencing organizational attractiveness in the Information Technology (IT) sector in Bangalore, India. A multistage sampling technique was employed to gather data from employees across twenty IT software companies in Bangalore. A structured questionnaire was administered, and a total of 740 responses were collected. Data analysis was conducted using the Statistical Programme for Social Sciences (SPSS 25.0), incorporating descriptive and inferential statistical methods. Exploratory factor analysis with Promax rotation was applied to extract the primary factors contributing to organizational attractiveness. The analysis revealed nine critical factors influencing organizational attractiveness: career growth opportunities (CGO), corporate social responsibility (CSR), flexible work practices (FWP), perceived organizational prestige (POP), perceived organizational support (POS), happiness at work (HAW), professional stability (PS), work options (WO), and compressed workweeks (CW). CGO and FWP emerged as the most impactful factors, reflecting employees' preferences for career advancement and work-life balance. CSR and POP highlight the importance of organizational values and reputation. The Author(s). -
Some properties of star-perfect graphs
For a finite simple graph G = (V, E), ?s(G) denotes the minimum number of induced stars contained in G such that the union of their vertex sets is V (G), and ?s(G) denotes the maximum number of vertices in G such that no two are contained in the same induced star of G. We call the graph G star-perfect if ?s(H) = ?s(H), for every induced subgraph H of G. We prove here that no cycle in a star-perfect graph has crossing chords and star-perfect graphs are planar. Also we present a few properties of star perfect graphs. 2026 Azarbaijan Shahid Madani University. -
On the zero forcing number of complementary prism graphs
The zero forcing number of a graph is the minimum cardinality among all the zero forcing sets of a graph G. The aim of this article is to compute the zero forcing number of complementary prism graphs. Some bounds on the zero forcing number of complementary prism graphs are presented. The remainder of this article discusses the following result. Let G and ? be connected graphs. Then Z(G?) ? n ? 1 if and only if there exists two vertices vi, vj ? V (G) and i 6? j such that, either N(vi) ? N(vj) or N[vi] ? N[vj] in G. 2025 Azarbaijan Shahid Madani University. -
Unveiling Future Trends in Employer Branding: Systematic Review and Bibliometric Analysis
Employer branding, an emerging area in Human Resource Management (HRM), has gained significant importance. Despite its importance, the literature on employer branding remains fragmented due to the absence of a comprehensive review that consolidates the intellectual structure of the field. This study addresses the existing knowledge gap by conducting a systematic literature review accompanied by bibliometric analysis utilizing performance analysis and science mapping through the Tableau software package. Through a comprehensive review of 27 articles, this study reveals the key branding elements, top journals, contributing countries, industries, citation trends, sample statistics, theoretical contribution, and six key themes (i.e., Employer branding attributes, sustainable employer branding, employee-centric employer branding, social media employer branding, recruitment strategies, HRM practices of employer branding) that characterize the body of the employer branding. Finally, the study has identified an integrative framework and set the direction for future research. It offers actionable recommendations for HR practitioners, emphasizing technology integration in employer branding initiatives and incorporating sustainable practices to enhance organizational attractiveness. This research contributes to a deeper understanding of the concept of employer branding. It provides valuable guidance for organizations seeking to navigate and optimize their employer branding strategies for the future. (2025), (Regional Inform. Center for Sci. and Technol.). All rights reserved. -
Role of Individualistic and Collectivistic Orientations in the Happy Life of Kharwar Adivasi Community
Following globalization, westernized cultural values, ideas, and practices have rapidly spread. Cultures are in flux, and indigenous communities are not free from the influence of the outside world. In this research, we investigated how the psychological tendencies of indigenous communities might be affected by such socio-cultural changes in a predominantly collectivist nation. A community-based study was conducted with 150 Kharwar Adivasi individuals residing in 10 villages of Naugarh block, Chandauli, Uttar Pradesh. The participants, aged 25-50 years, were given the measures of Individualism-Collectivism Orientations and Happy Life. Using an exploratory factor analysis, a five-factor structure emerged, explaining 57% of the variance in happy life. The results indicated that 59% of the sample had a collectivistic orientation. Individuals with a collectivistic orientation fared better in overall happiness and its sub-domains than individuals with an individualistic orientation. It is suggested that even though there is a gradual increase in individualism, for the Adivasi community, happiness is still enhanced by tendencies of interdependence. The findings have important implications for understanding the happiness of the under-researched Adivasi population. (2025), (School of Management Sciences). All rights reserved. -
THE CONFLICT CATALYST: IHL'S ROLE WHEN CLIMATE CHANGE TRIGGERS DISPLACEMENT
The escalating climate crisis is profoundly reshaping global human mobility, forcing millions to abandon their homes due to both sudden-onset disasters and insidious slow-onset environmental degradation. This paper examines how international humanitarian law (IHL) and climate-induced displacement are related, particularly when armed conflict intensifies or intersects with the consequences of climate change. Despite the informal usage of the term climate refugee, there is a significant protection gap because the 1951 Refugee Convention does not give it a legal designation. While IHL is primarily designed to regulate armed conflict and protect its victims, this research argues that its principles and provisions become indirectly, yet crucially, relevant when climate change acts as a threat multiplier, intensifying existing conflicts or creating new fragilities that lead to displacement. Through a qualitative legal analysis complemented by three diverse case studies, the Sunderbans (India and Bangladesh), the Lake Chad Basin, and Somalia/Horn of Africa. The paper aims to critically analyse the applicability and limitations of International Humanitarian Law in addressing climate-induced displacement, particularly in contexts where climate change acts as a threat multiplier for armed conflict. Through a case-based legal analysis, the article seeks to demonstrate how existing legal frameworks fall short of providing adequate protection for climate-displaced persons and to situate IHL within a broader matrix of human rights, migration, and climate governance regimes. 2025 Brawijaya Law Journal. -
AeroGlan: A Smart and Sustainable Plant Species Estimator For Organic And Localized Air Filtering
Introduction: Human health is significantly compromised by air pollution, especially by local air quality. The majority of our society spends their lives in a confined geographical location, which if subjected to air pollution can expose them to long-term air contamination. It is also possible that poor air quality can pose serious health risks, especially to susceptible individuals thereby impacting their lifestyle. Air quality can be improved with appropriate plantation, but they are underutilized. Various air purification devices have been developed in response to the ever-increasing air pollution level. Methods: However, artificial means of air purification are not very viable in terms of cost, accessibility to society, and reliable tools to purify air. This research integrates traditional solutions with modern technology to counter air purification by selectively using plant species and placing them in desired locations suitable for urban settings. The study aims to measure the constituents of various air pollutants spanning across regions to identify and accumulate pollution data using IoT-based smart devices, remit, and feed this information to cloud-based storage for further processing. In addition, advanced predictive intelligence is utilized to determine the plant species that can suffice the need for air purification through organic means in a given geographical zone resulting in enhancement of Air Quality (AQ), with minimal cost, prolonged shelf life, future proof and non-detrimental consequences. Results: Implementation outcome gives a promising outcome. Accurate readings of various air pollutants are aggregated. Suitable trees are identified to tackle these pollutants and their absorbing capacity is determined. Various predictive methods are employed and the random forest model recorded the best results. The sensory units of the model successfully captured the pollutant data and any major fluctuations were reported. The prediction pipeline recorded a mean precision, recall, and f-score value of about 0.95, 0.92, and 0.94 respectively while the mean accuracy of 0.965 was also noted. The observed training and validation accuracy with our model were 0.96 and 0.93 respectively. Conclusion: Hence, the proposed AeroGlan model may be locally applied as an air pollutants monitoring device and also to suggest suitable plant species required to counter air contamination in that locality. 2025, Bentham Science Publishers -
Associations Between Early Life Adversity, Moral Development, and Psychopathology in Children and Adolescents: A Cross-Sectional Study
Introduction: Moral psychological development is shaped by socio-cultural and neurobiological factors, with the formation of conscience central to this process. Early Adverse Childhood Experiences (ACEs) have been linked to delays in moral development and increased risk of psychiatric disorders. This study examined how adversity affects conscience functioning, specifically the association between Psychopathological Interference (PI) and delays in Conscience Stages (CS) compared to youth raised in relative advantage. Methods: We analyzed 125 conscience-sensitive psychiatric interviews with youth admitted to a Psychiatric Residential Treatment Facility (PRTF). CS scores were compared with expected stages from community youth, using the Conscience Development Quotient (CDQ = CS attained CS expected 100). PI was rated on a Likert scale, incorporating full psychiatric evaluations, behavioral ratings, and DSM diagnoses. Multiple regression models examined the associations between CDQ, PI, and Clinical Global Assessment of Functioning (CGAF) scores, controlling for six covariates. Results: Participants (mean age, 14.2 years; 59% male, 41% female) exhibited significantly greater distress signals across conscience domains compared to community youth. No differences emerged by age at the onset of ACE. However, lower CDQ was associated with higher PI, earlier ACE onset, DSM Axis II disorders, and lower CGAF. Legal history and ACE count were not significant predictors. The model explained 22.7% of the variance in CDQ (p = 0.00018). Discussion: Findings highlight CDQ as a sensitive measure of developmental impact, beyond simply identifying red flags, consistent with prior ACE research. Retrospective design may limit sensitivity to ACE characteristics. Conclusion: Systematic conscience-sensitive interviewing, attuned to cultural and developmental contexts, may enhance clinical assessment of moral functioning. 2025, Bentham Science Publishers -
Assessing the Impact of E-learning through Usage and Preference of E-resources
Aims: Any electronic device that delivers a collection of data, whether it be text referring to full text databases, electronic journals, photographs, other multimedia goods, or quantitative, visualizations, or time-based, is referred to as an electronic resource. These could be transmitted over the internet, tape, CD-ROM, tablets, smartphones, smart watches or another medium, these are now the basis of e-learning. Online searching has made it possible to get patent information more quickly, affordably, and conveniently than the traditional manual or CD-ROM based searching method. The ability to create and distribute documents in electronic form is now made possible by a number of established procedures and standards. So, in order to address the current problems, librarians are utilizing new media, particularly electronic resources, in their collection expansion makes the documentation of users better. As we can see, utilizing online resources is important in the modern world for a multitude of purposes. Because of this, it's important to understand the preferences, motives and usage of various e- resources used by students who use online learning. The aim of the present research paper was to examine the impact of e-resources using its usage and reading preferences. In this study, reasons such as time saving, more information, and busy schedule at college are considered. Methodology: Primary data was gathered from 250 students from Mumbai and Navi Mumbai who are using e-resources through the pre-structured questionnaire. The responses collected were recorded using the SPSS software for data analysis. In order to examine the link between causes, preferences, and the use of e-resources, a theoretical construct was developed grounded on a few assumptions. Statistical techniques like the chi-square test were used and data analysis was done using SPSS version 20 to examine the proposed construct. When doing the data analysis, the demographic profile, objectives, and hypothesis were all taken into consideration. Results: The average for each component that is time saving, more informative, and busy schedule at college was computed and was determined as 0.004, 0.004, and 0.000, correspondingly, for time saving, more informative content, and busy college schedule. As all of these values for all of the preferences under consideration are less than 0.05, it is clear that there is a connection between the usage of electronic resources and their underlying reasons and preferences. Conclusion: Hence, there is a substantial correlation between the reasons for using electronic resources and the different reading preferences, as well as between the two. Only three reasons namely time saving, more informative, and busy schedule at college are considered during this study. Data collection is done from Mumbai and Navi Mumbai region only. 2025 Bentham Science Publishers. -
Hybrid Deep Learning Framework for Continuous Blood Glucose Monitoring and Gestational Diabetes Risk Prediction
Gestational diabetes mellitus (GDM) affects almost 10%-12% of pregnancies worldwide, threatening maternal and fetal life. Continuous glucose monitoring (CGM) forms the backbone of managing GDM, and the current methodologies largely disregard physiological and behavioral factors, thereby greatly reducing accuracy and clinical interpretability. Methods: A hybrid deep learning framework was developed by fusing CGM with multi-sensing modality data, including heart rate, activity levels, sleep patterns, and dietary intake. For data preprocessing, Kalman filtering was applied for temporal alignment, adaptive normalization provided outlier handling and imputation, while the CNN-BiLSTM backbone with attention was harnessed for feature extraction. A Multi-Task Attention Fusion Network (MTAFN) was used to predict glucose values and classify GDM risk simultaneously, while SHAP and dynamic smoothing contributed to interpretability sets. Results: The framework was validated on an extended OhioT1DM dataset with adaptations for pregnancy. It reached a glucose prediction RMSE of 9.8 mg/dL and a GDM risk classification accuracy of 93%. Compared to competitive approaches, the present solution attained a 25% better accuracy on interpretability and an improvement in sensitivity and specificity of about 4-6% across various physiological conditions. Discussion: The use of multi-sensing data increased prediction robustness by capturing complex physiological dependencies. The SHAP-based interpretability justified the predictions through a physiological lens. With an attention mechanism for feature weighting, it was possible to identify crucial variables like meal intake and nighttime variability in the workflow sets. Conclusion: The hybrid framework proposed here is reliable for clinically interpretable continuous glucose monitoring and GDM risk predictions. Its application with high reliability can lead to integrating it within clinical protocols for real-time maternal care sets. 2026, The Author(s). This is an open access article distributed under the terms of the Creative Commons Attribution 4.0 International Public License (CC-BY 4.0), a copy of which is available at: https://creativecommons.org/licenses/by/4.0/legalcode. This license permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. -
Harary Spectra and Energy of Certain Classes of Graphs
Aims: To investigate the H-eigenvalues and H-energy of various types of graphs, including k-fold graphs, strong k-fold graphs, and extended bipartite double graphs and establish relationships between the H-energy of k-fold and strong k-fold graphs and the H-energy of the original graph G, we explore the connection between the H-energy of extended bipartite double graphs and their ordinary energy and find the graphs that share equienergetic properties with respect to both the ordinary and Harary matrices. Background: The H-eigenvalues of a graph G are the eigenvalues of its Harary matrix H(G). The H-energy {Formula Presented} of a graph, G is the sum of the absolute values of its H-eigenvalues. Two connected graphs are said to be H-equienergetic if they have equal H-energies. They are said to A-equienergetic if they have equal A-energies. Adjacency and Harary matrices have applications in chemistry, such as finding total electron energy, quantitative structure-property relationship (QSPR), etc. Objectives: We determined the H-spectra of k-fold graphs, strong k-fold graphs and extended bipartite double graphs and established connections between the H-energy of different types of graphs and their original graph G for investigating the relationship between the H-energy of extended bipartite double graphs and their ordinary energy and the graphs that share equienergetic properties with respect to both the adjacency and Harary matrices. Methods: Spectral algebraic techniques are used to calculate the H-eigenvalues and H-energy for each type of graph and compare the H-energies of different graphs to identify the equienergetic properties and derive relationships between the H-energy of extended double cover graphs and their ordinary energy. Results: We determined the H-spectra of k-fold graphs, strong k-fold graphs and extended bipartite double graphs and established relationships between the H-energy of k-fold and strong k-fold graphs and the H-energy of the original graph G. Then, we explored the connection between the H-energy of extended bipartite double graphs and their ordinary energy and presented graphs demonstrating equienergetic properties concerning both adjacency and Harary matrices. Conclusion: The study provides insights into the H-eigenvalues, H-energy and equienergetic properties of various types of graphs. The established relationships and connections contribute to a deeper understanding of graph spectra and energy properties and the findings enhance the theoretical framework for analyzing equienergetic graphs and their spectral properties. Scope: Possible extensions of this research could include investigating additional types of graphs and exploring further explicit connections between different graph energies and spectral properties. Harary matrices are distance-based matrices, which can model distances between atoms in molecular structures and could be useful in organic synthesis to predict how molecular structures behave. 2025, Bentham Science Publishers -
Optimizing Functional Feed for Growth and Pathogen Resistance in Oreochromis niloticus using Fermented Seaweeds: A Comprehensive Approach Through Solid State Fermentation and Oxidative Stress Response
The study aimed to explore the potential of seaweeds Sargassum wightii and Gracilaria corticate fermented using Bacillus subtilis MN960600 (CK4). Fermented seaweeds showed enhanced antioxidant activity in DPPH assays. A second-order model known as Box-Behnken was used to create an optimized quadratic design for fermentation parameters enhancing protein, reducing sugars, and lipid yields. This optimized feed demonstrated significant growth improvement of 18 to 20 % in Oreochromis niloticus when compared to commercial feed and a 35 to 40% higher growth in fermented and non-fermented feed groups. Additionally, fish fed formulated seaweeds exhibited resilience to Vibrio harveyi and Aeromonas hydrophila pathogen stress. Additionally, the study highlighted the ability of the formulated seaweed in reduction of oxidative stress caused by pathogens Vibrio harveyi and Aeromonas hydrophila in Oreochromis niloticus. The study emphasized the potential use of seaweeds and probiotic bacteria as a sustainable aquafeed. 2025, Egyptian Society for the Development of Fisheries and Human Health. All rights reserved.