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A Study on Coloring Parameters and Topological Indices of Graphs
Graph coloring/labeling is a fundamental concept in graph theory that involves the assignment of weights, integers, or colors to the vertices/edges or both of a graph while adhering to specifc constraints. Graph colorings serve as a powerful mathematical model with broad applications in real-world scenarios, including network analysis, genomics, routing, optimization techniques, and digital networks. A research domain is established in which vertices of a graph are colored based on specifc conditions, and color degrees are taken into consideration leading to the exploration of chromatic topological indices and various chromatic polynomials. The introduction of chromatic topological indices in response to challenges in chemical graph theory has sparked signifcant research interest, creating a dynamic and expansive feld within graph theory. Motivated by this our study presents a comprehensive exploration of topological indices in the context of graph theory, specifcally focusing on the Zagreb index and its chromatic variants. The study calculates the frst and second rainbow chromatic Zagreb indices, rainbow chromatic irregularity indices, and rainbow chromatic total irregularity indices for well-known graph classes. Later, introduced the concept of b-chromatic Zagreb indices and b-chromatic irregularity indices and calculated the exact values for some standard graphs. Further, the rainbow chromatic topological indices and b-chromatic topological indices for various newlinederived graphs such as line, middle, total, and central graphs of some graph classes are determined. Novel graph polynomials, namely the b-chromatic Zagreb polynomials and b-chromatic irregularity polynomials, are introduced for some classes of graphs and the derived graphs such as degree splitting graph, mycielski graph. This comprehensive approach not only enhances our theoretical understanding of graph coloring but also oand#64256;ers practical insights into the predictive power of chromatic topological indices in diverse chemical contexts. -
RAINBOW CHROMATIC TOPOLOGICAL INDICES OF CENTRAL GRAPHS OF SOME GRAPHS
The chromatic topological indices concept was introduced recently. Many other variations concerning the chromatic topological indices have been studied lately. In this paper, we have calculated the first and second rainbow chromatic Zagreb indices and rainbow chromatic irregularity indices for central graph of some standard graph classes. Palestine Polytechnic University-PPU 2024. -
COMPUTATION OF b-CHROMATIC TOPOLOGICAL INDICES OF SOME GRAPHS AND ITS DERIVED GRAPHS
The two fastest-growing subfields of graph theory are graph coloring and topological indices. Graph coloring is assigning the colors/values to the edges/vertices or both. A proper coloring of the graph G is assigning colors/values to the vertices/edges or both so that no two adjacent vertices/edges share the same color/value. Recently, studies involving Chromatic Topological indices that dealt with different graph coloring were studied. In such studies, the vertex degrees get replaced with the colors, and the computation is carried out based on the topological index of our choice. We focus on b-Chromatic Zagreb indices and b-Chromatic irregularity indices in this work. This paper discusses the b-Chromatic Zagreb indices and b-Chromatic irregularity indices of the gear graph, star graph, and its derived graphs such as the line and middle graph. 2023, RAMANUJAN SOCIETY OF MATHEMATICS AND MATHEMATICAL SCIENCES. All rights reserved. -
QSPR Analysis On Octane Isomers Using Degree-Based Topological Indices?
Octane isomers are structures with the chemical formula C8H18. Despite having the same formula, they have variations in the way their atoms are arranged, leading to differences in their chemical and physical properties. In this paper, we conduct a QSPR analysis on various isomers of octane, focusing on specific degree-based topological indices. In QSPR studies, these measures, known as topological indices, are helpful in understanding and quantifying the biological effects of chemical compounds. We specifically look at how certain properties of octane, such as complexity, acentric factor, standard enthalpy of vaporization, entropy, and enthalpy of vaporization, are connected to these topological indices. Our research provides valuable insights into how these indices can predict the behavior of octane isomers, contributing to a better overall understanding of their properties. 2024, Tsing Hua University. All rights reserved. -
Some results on b-chromatic topological indices of some graphs
Graph coloring is assigning weights, integers, or colors to edges, vertices, or both in a graph subject to certain conditions. Proper coloring C of graph G refers to assigning weights, integers, or colors to the vertices, edges, or both so that adjacent vertices or adjacent edges get a different color. A b-coloring follows proper vertex coloring with subject to an additional property that each color class should have at least one vertex with a neighbor in all the other color classes. The notion of Chromatic Zagreb index and irregularity index was introduced recently. This paper introduces the concept of b-Chromatic Zagreb indices and b-Chromatic irregularity indices. Also, we compute these indices for certain standard classes of graphs. 2023 Author(s). -
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Cultural Constraints and Empowerment: A Study of Kudumbashree in Kerala
Women empowerment occupies the centre of discussions of social development and is carried by UNDP (United Nations Development Programme). It continues to be highly debated and contested. Different scholars have defined empowerment in a different ways depending upon the contextual variations. The study seeks to present varied theoretical perspectives on empowerment and reinforce them with current empowerment practices in Indian settings. Based on relevant literature on empowerment, an attempt has been made here to examine the definitions and its cultural and contextual variations. This provides a linkage between theory and practice of empowerment in Indian society. An ethnographic study of Kudumbashree, a women organization in Kerala is been carried out where the contextual variations of empowerment is covered. Women empowerment has multiple implications for patriarchal surroundings and has possessed problems in re-engaging with structural inequalities like caste and class identities of women. All these create a plethora of problems to Indian society and empowerment among women helps in solving and eradicating such problems. Hence the study attempts to find out how Kudumbashree negotiates the contextual and structural issues of women empowerment. The problems faced by women tend to increase day by day and studying topics likes these helps in minimizing it thereby providing a better understanding about the concept of women empowerment. The researcher concludes the study by mentioning the contextual and dynamic variations of empowerment. There is no universally accepted definition for empowerment where it varies according to the subjective locations of individuals. For instance; empowerment for a woman in a scheduled caste or lower caste women varies to that of upper caste women. -
Addressing quarter life crisis as a public health priority
The Quarter-Life Crisis (QLC), a period of intense self-doubt, anxiety, and identity confusion during early adulthood has become a widespread phenomenon affecting mental health and well-being globally. In the Indian context, this phase is further shaped by cultural expectations, economic uncertainty, and social transitions that shape young adults sense of purpose and stability. Although often discussed in psychological and sociological terms, the QLC remains under-addressed in public health discourse. This perspective paper argues for the recognition of QLC as a legitimate public health issue with cross-sector implications. Economic precarity, including unstable employment, student debt, and housing insecurity, plays a critical role in exacerbating this crisis, making it not only a psychological experience but also a condition influenced by broader socioeconomic and cultural forces. Drawing on developmental psychology, sociocultural theory, and the framework of the Sustainable Development Goals (SDGs), this paper situates the Quarter-Life Crisis within Indias evolving social landscape and examines it as a social determinant of mental health. It further highlights community-based and digital interventions, such as resilience and self-compassion apps, that can support young adults. Integrating QLC into public health frameworks particularly those focused on Good Health and Well-Being (SDG 3) can offer timely, systemic solutions to a rising mental health concern among Indias youth and the global young adult population. The Author(s) 2026. -
Quadratic convective transport of Cu-Al2O3 hybrid nanoliquid with Hall current, variable suction, and exponential heat source
The time-dependent slip flow and heat transport of the Cu-Al2O3 hybrid nanofluid through a vertical permeable plate with Hall current and variable suction is investigated. An exponential heat source and quadratic convection effects are considered. The dimensionless governing equations are solved analytically using the regular perturbation method. The graph of variation of the different flow fields with respect to the distance from the plate is drawn for the analysis. It is established that the exponential heat source aspect increased the temperature profile while the quadratic convection aspect decreased the temperature profile. The applied magnetic field and nonlinear convection aspects reduce the axial velocity field. The quadratic convection and exponential space-dependent heat source phenomena are favorable to friction factors. Furthermore, the global heat transfer is increased in the presence of an exponential space dependent heat source and hybrid nanoparticles. 2021 John Wiley & Sons, Ltd. -
Parental Psychological Distress of Missed Diagnosis of Down Syndrome at Antenatal Screening: A Rare, but Still Real Occurrence-A Case Report and Review of Literature
Introduction: Prenatal screening programs are important components for pregnant women care and are often linked with grief and shock based on gestational age or the diagnosis. Lower/no sensitivity is also associated with these screening programs leading to providing false-negative outputs. Case Presentation: Present work shows a case of missed antenatal diagnosis of Down syndrome and its persistant medical and psychological impact on the family members. We have also discussed the relevant economic and medical-legal issues related to the context and aimed to maintain an adequate awareness among healthcare to discuss properly these investigations (difference between screening and diagnostic testing), their possible outcome (chances of false results) and enabled the pregnant women/couple to take informed decision on early pregnancy. Conclusion: These programs are considered as routine clinical practice in many countries from last few years and are necessary to assess the pros and cons of these programs. One of the prime cons involves the likeliness of obtaining a false-negative result due to lack of 100% sensitivity and specificity. 2023 S. Karger AG, Basel. -
Toxic waste colonialism : A re-evaluation of global management of transboundary hazardous waste /
Journal On Environment Law Policy And Development, Vol.3, pp.85-119, ISSN: 2348-7046. -
Mining the web data for classifying and predicting users' requests
Consumers are the most important asset of any organization. The commercial activity of an organization booms with the presence of a loyal customer who is visibly content with the product and services being offered. In a dynamic market, understanding variations in client?s behavior can help executives establish operative promotional campaigns. A good number of new consumers are frequently picked up by traders during promotions. Though, several of these engrossed consumers are one-time deal seekers, the promotions undeniably leave a positive impact on sales. It is crucial for traders to identify who can be converted to loyal consumer and then have them patronize products and services to reduce the promotion cost and increase the return on investments. This study integrates a classifier that allows prediction of the type of purchase that a customer would make, as well as the number of visits that he/she would make during a year. The proposed model also creates outlines of users and brands or items used by them. These outlines may not be useful only for this particular prediction task, but could also be used for other important tasks in e-commerce, such as client segmentation, product recommendation and client base growth for brands. Copyright 2018 Institute of Advanced Engineering and Science. All rights reserved. -
An Investigation into the Effects of Varying Seasons, Indole-3-Butyric Acid (IBA) and Rooting Media on the Rooting and Longevity of Air-layered Water Apples (Syzygium samarangense L.)
Background: The variation observed in sexual propagation often results in slow growth and fruit development, attributed partly to insufficient photosynthates during early growth stages. To address this challenge, vegetative propagation methods such as air layering offer promising solutions. This technique not only accelerates productivity but also enhances the quality of water apples. Recognizing the importance of air layering in water apple cultivation, this experiment was conducted to standardize this technique by examining the impact of different seasons and planting media in the western tropical wet and dry climate of Tamil Nadu. Methods: The study was conducted to evaluate the variables affecting air layering in water apples in Coimbatore district. The experiment was carried out with three different factors like seasons [August (S1), September (S2) and October (S3)] and IBA [applied at different concentrations of 2000 mg/L (I1), 3000 mg/L (I2) and 4000 mg/L (I3)] along with different rooting media: Cocopeat (M1) and Sphagnum moss (M2). The factorial randomized complete block design (FRCBD) was laid out for statistical analysis. Result: Sphagnum moss performed as a better rooting medium due to its high water holding capacity and good aeration. Increase in the number and early formation of roots were due to more rain fall and high relative humidity in August, that resulted in more nutrient uptake and structural stability. The discovery aids in determining the optimal conditions, including season, dosage and combination (4000 mg/L IBA with sphagnum moss applied in August), for successful air layering in water apple. 2025, Agricultural Research Communication Centre. All rights reserved. -
Supply chain leadership in emerging markets: Understanding the role of trust, information management, and collaboration
The massive growth of emerging economies in last two decades has attracted many global companies to expand their physical presence in these countries. But the ability to take advantage of those opportunities is only available to companies that appreciate the environmental challenges and complexity of the region. The lexicon of extant literature focuses on enhancing supply chain leadership and development of efficient and effective strategies in developed economies, yet the corresponding literature in emerging economies is very fragmented. The aim of this chapter is to synthesize the current literature to understand the phenomenon including its definitions, dimensions, and constructs and to propose a conceptual model for successful supply chain leadership in emerging markets. The study tries to understand and establish the impact of various factors of supply chain leadership, which leads to sustainable supply chain performance. Collaboration and information management emerge as the major drivers for supply chain leadership in emerging markets and identifies trust as a mediating factor. 2020 by IGI Global. All rights reserved. -
Spin Frequency of Neutron Star in the Bright Atoll Source 4U 1705-44 Using NICER Observation
We conducted a systematic study of two thermonuclear type I X-ray bursts (B1 and B2) and the spectral properties of the bright atoll type neutron star low-mass X-ray binary 4U 1705?44 using NICER observation. In our analysis, a burst oscillation at ?702 Hz was detected during the double-peaked profile of burst B1. This provides the first strong evidence for the spin frequency of the neutron star, which establishes 4U 1705?44 as a rapid rotator. The measured convexity parameters of the bursts indicate that both bursts likely ignited at off-equatorial latitudes. The ignition depth of burst B1 was nearly twice that of B2, indicating substantial fuel consumption between the two events. The recurrence time of B2 (?1 hr) categorizes it as a short waiting time burst. The complementary spectral analysis of persistent emission, modeled with tbabsnthcomp+ diskbb), showed a hard state with a photon index ? < 1.12. The hardnessintensity diagram was consistent with the source being in the island state. Notably, the accretion disk appeared to extend close to the neutron star surface. 2026. The Author(s). Published by the American Astronomical Society. -
AstroSat's view of kHz quasi-periodic oscillations from 4U 1820?30
This study presents the spectro-temporal analysis of the neutron star low mass X-ray binary 4U 1820?30, using data from three observations conducted by AstroSat 's Soft X-ray Telescope and Large Array X-ray Proportional Counter. Spectral analysis revealed that the source spectra could be modelled using an absorbed blackbody and a multi-temperature disk model along with a Comptonization model with ?=1.24 ? 1.89 and the inner accretion disk located at an distance of ?17 km from the neutron star. This showed the source to be in the hard spectral state. Temporal analysis revealed the presence of kHz quasi-periodic oscillations (QPOs) with frequencies in the 640 ? 1090 Hz range with root mean squared (RMS) amplitudes between 6 ? 10 per cent and quality factors between 8 ? 42. The RMS amplitude?energy and time lag?energy spectra of the upper and lower kHz QPOs hint them to be caused by modulations of photons having a common radiative mechanism. Moreover, the maximum RMS amplitude and time lag exhibited an anti-correlation with mass accretion rate. Using an analytical relation based on the relativistic precession model, the mass of the neutron star in the system was estimated to be 1.8 M?. The emission radius of one of the detected kHz QPOs was estimated to be ? 17 km. 2025 Elsevier B.V. -
Spectral and temporal features of GX 13+1 as revealed by AstroSat
GX 13+1, a neutron star low-mass X-ray binary that exhibits the properties of both atoll and Z sources, is studied using data from Soft X-ray Telescope and Large Area X-ray Proportional Counter (LAXPC) onboard AstroSat. The source traces a ? shaped track in its hardness-intensity diagram (HID). Spectral modelling of the data in the 0.7-30.0 keV energy range, with the model-+, yields orbital inclination angle (?) of 77. Flux resolved spectral analysis reveals the ? shaped pattern in the plots of spectral parameters kTe, kTbb, and ? versus Fbol, closely resembling the pattern traced in LAXPC HID. This indicates changes in the spectral properties of the corona and the boundary layer/accretion disc. Assuming that the accretion disc truncates at the AlfvCrossed D sign n radius, the upper limit of the magnetic field strength (B) at the poles of neutron star in GX 13+1 is calculated to be 5.10 108 G (for kA = 1 and ? = 0.1), which is close to that of atoll sources. Furthermore, thickness of the boundary layer is estimated to be 5.70 km, which results in the neutron star radius value of 14.50 km. Quasi-periodic oscillations (QPOs) at 56 4 and 54 4 Hz are detected in Regions D and E of HID, respectively. The frequencies of these QPOs are similar to the characteristic frequency of horizontal branch oscillation and these do not exhibit a positive correlation with mass accretion rate. -
Mayfly Algorithm for Optimal Integration of Hybrid Photovoltaic / Battery Energy Storage / D-STATCOM System for Islanding Operation
In today's power system design studies, autonomous and self-healing capabilities are becoming increasingly important. Renewable energy (RE) integration, on the other hand, is geared at long-term sustainability. In this regard, a hybrid energy system consisting of a photovoltaic (PV) source, battery energy storage (BESS), and distribution-static synchronous compensator (D-STATCOM) is proposed for optimal design and integration in the electrical distribution network (EDN) when short-term islanding operational requirements are taken into account. When considering grid-connected mode, the PV system is initially optimally allocated towards loss minimization. Following that, the capacities of BESS and D-STATCOM are assessed in the context of a short-term islanding scenario. The optimization problem is tackled utilising a recent meta-heuristic mayfly optimization algorithm (MOA) in both stages. The simulations are run on an IEEE 33-bus EDN network. By having optimal PV system in grid-connected mode, it is observed that real power losses are reduced to 111.03 kW from 210.998 kW and reactive power losses are reduced to 81.684 kVAr from 143.033 kVAr. In addition, the minimum voltage in the network is raised to 0.9424 p.u. from 0.9038 p.u. On the other hand, by designing hybrid energy systems using PV, BESS, and D-STATCOM, the network is able to serve the entire load even under islanding conditions. MOA's competitiveness in solving difficult non-linear multivariable optimization problems was demonstrated in comparative research with literature publications. In addition, the proposed hybrid energy system can cope with the uncertainties and other requirements of current grids. 2022. All Rights Reserved. -
The Middle Class in India Trends and Patterns
The middle class in India is an economically significant group, the composition of which is very diverse. Researchers often use income as an indicator to identify or measure the middle class. This article uses consumption as an indicator based on the purchasing power parity to identify the middle class. Further, it categorises the middle class into different groups based on their economic standing within its class, from the emerging middle class to the higher middle class. 2025 Economic and Political Weekly. All rights reserved. -
Deep-fake Detection for Recognising Altered Audio using Deep Learning Approach
Ensuring the validity of audio recordings is becoming increasingly difficult due to deep-fake technology. Audio-analysis is used to identify deep-fake audio, which has been examined here. Machine-learning models can be made technological to compare between real and modified audio by examining minute artifacts and inconsistencies added to during the deep-fake production process. In this work, advanced signal-processing techniques like spectrum-analysis, voice-activity detection, and speaker-recognition; are used to extract relevant information from audio recordings. In order to exact deep-fake audio detection, these features are then utilized to guide and judge deep-learning models, such as recurrent neural networks (RNNs) and convolutional neural networks (CNNs). The objective is to create reliable and efficient techniques for detecting altered audio, almost eliminating the possible dangers. The goal is to provide reliable and efficient techniques for detecting modified audio in order to mitigate the possible risks related to deep-fake technology in a number of fields, such as social-media, journalism, and security. 2025 IEEE.