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                <text>Heat transfer and entropy generation analysis of non-Newtonian fluid flow through vertical microchannel with convective boundary condition</text>
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                <text>Bejan number; Entropy generation; Mag- netic field; Microchannel; Third-grade fluid</text>
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                <text>The entropy generation and heat transfer characteristics of magnetohydro-dynamic (MHD) third-grade fluid flow through a vertical porous microchannel with a convective boundary condition are analyzed. Entropy generation due to flow of MHD non-Newtonian third-grade fluid within a microchannel and temperature-dependent viscosity is studied using the entropy generation rate and Vogels model. The equations describing flow and heat transport along with boundary conditions are first made di-mensionless using proper non-dimensional transformations and then solved numerically via the finite element method (FEM). An appropriate comparison is made with the pre-viously published results in the literature as a limiting case of the considered problem. The comparison confirms excellent agreement. The effects of the Grashof number, the Hartmann number, the Biot number, the exponential space-and thermal-dependent heat source (ESHS/THS) parameters, and the viscous dissipation parameter on the temperature and velocity are studied and presented graphically. The entropy generation and the Bejan number are also calculated. From the comprehensive parametric study, it is recognized that the production of entropy can be improved with convective heating and viscous dissipation aspects. It is also found that the ESHS aspect dominates the THS aspect.  Shanghai University and Springer-Verlag GmbH Germany, part of Springer Nature 2019.</text>
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                <text>Madhu M.; Shashikumar N.S.; Mahanthesh B.; Gireesha B.J.; Kishan N.</text>
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                <text>Applied Mathematics and Mechanics (English Edition), Vol-40, No. 9, pp. 1285-1300.</text>
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                <text>ISSN: 2534827; CODEN: AMMEE</text>
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                <text>Madhu M., Department of Studies and Research in Mathematics, Kuvempu University, Shankaraghatta, 577451, India; Shashikumar N.S., Department of Studies and Research in Mathematics, Kuvempu University, Shankaraghatta, 577451, India; Mahanthesh B., Department of Mathematics, Christ Deemed to be University, Bangalore, 560029, India; Gireesha B.J., Department of Studies and Research in Mathematics, Kuvempu University, Shankaraghatta, 577451, India; Kishan N., Department of Mathematics, Osmania University, 500007, Telangana, India</text>
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                <text>Irreversibility analysis of the MHD Williamson fluid flow through a microchannel with thermal radiation</text>
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                <text>entropy generation; Finite element method; microchannel; thermal radiation; Williamson fluid</text>
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                <text>The heat transport and non-Newtonian fluid (Williamson fluid) flow through a micro-channel are considered to analyze the entropy generation minimization using the thermodynamic second law. The energy equations have been modeled with the addition of joule heating, heat source, and thermal radiation. The use of suitable dimensionless transformation helps to convert the modeled flow equations into non-dimensional coupled ODEs. The numerical simulations are done via the Finite Element Method. The current outcomes are constructed to examine the behavior of various flow parameters and presented via graphs. It is found that the rise of heat source and Reynolds number Re decays/boosts the entropy rate Ns and the Bejan number Be profile near the left/right plate, and reverse behavior is noticed for the thermal radiation parameter.  2022 Informa UK Limited, trading as Taylor &amp;amp; Francis Group.</text>
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                <text>Madhu M.; Shashikumar N.S.; Thriveni K.; Gireesha B.J.; Mahanthesh B.</text>
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                <text>Waves in Random and Complex Media</text>
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                <text>ISSN: 17455030</text>
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                <text>Madhu M., Department of Mathematics, Chaitanya Bharathi Institute of Technology, Hyderabad, India; Shashikumar N.S., Department of Mathematics, Malnad College of Engineering, Hassan, India; Thriveni K., Department of Mathematics, CHRIST (Deemed to be University), Bangalore, India; Gireesha B.J., Department of Mathematics, Kuvempu University, Shimoga, India; Mahanthesh B., Department of Mathematics, CHRIST (Deemed to be University), Bangalore, India</text>
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                <text>Covid-19 Classification and Detection Model using Deep Learning</text>
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                <text>Classification; Convolutional Neural Network; COVID 19; Darknet model; Deep Learning; pneumonia</text>
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                <text>One of the deadly diseases in recent years is covid19 which is affecting the lives of peoples. Also leading to severe adverse problems and death. Prevention is done using early diagnosis and medication which in turn helps in early detection of the disease. The basic aim of the paper is to identify and further classify the patients using the chest x-rays. From scratch the Convolutional Neural Network is diagnosed producing a very high accurate and optimum results. In recent years, researchers found out that in the radiological images such as like x-rays, the traces of covid-19 can be found. In few areas, a good accuracy of the covid-19 detection cannot be achieved due to lack of the people who test so the artificial intelligence is combined with the radiological image. In machine learning the models used are deep learning by automatizing the actions and making it certain by swift, skillful and proficient outcome produced by the chest images provided by the patients. There are several layers like convolutional layer, max pooling layer etc. which are initiated and are used with aid of ReLU activation function. These images given as inputs are also classified accordingly. There is a sequence of neurons being given as input to the active dense layer and there is a result to the input by a sigmoidal function. There is a rise in efficiency because the models are trained and there is a decline of loss at the same time. If there is a model where fitting is done earlier to the overfitting and is restricted from implementing in the data augmentation. There is a better and efficient involvement of suggestions to models of deep learning. Further there is a classification of chest images for identifying and analyzing covid19. So, to check the Covid detection, the images are used as raw. In this paper a model is proposed to have good accuracy in the classification between Covid and normal and further it can be classified into three categories like Covid, pneumonia, normal. There is a 98.08% for the first one and 87.02% for the second one. By introducing 17 convolutional layers and using the Darknet model used for classifying you only look once (YOLO) for the live identification of the objects and multiple layers of filters are used. In the model there is an initial screening.  2022 IEEE.</text>
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                <text>Madhu M.; Xavier A.; Jayapandian N.</text>
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                <text>Proceedings of the International Conference on Electronics and Renewable Systems, ICEARS 2022, pp. 1457-1462.</text>
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                <text>Institute of Electrical and Electronics Engineers Inc.</text>
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                <text>&lt;a href="https://doi.org/10.1109/ICEARS53579.2022.9752290" target="_blank" rel="noreferrer noopener"&gt;https://doi.org/10.1109/ICEARS53579.2022.9752290&lt;/a&gt;
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                <text>Madhu M., School of Engineering and Technology Christ (Deemed to Be University), Bangalore, India; Xavier A., School of Engineering and Technology Christ (Deemed to Be University), Bangalore, India; Jayapandian N., School of Engineering and Technology Christ (Deemed to Be University), Bangalore, India</text>
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                <text>Master of Arts in Media and Communication Studies</text>
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                <text>Film alludes to an arrangement of pictures moving constantly, in a steady progression which makes an illusionary impact of development. Ranjith is a Malayalam screenwriter, filmmaker, producer and actor. The researcher here aims to analyse four films by Director Ranjith and study the audience perception or understanding on films related social issues.</text>
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                <text>Digital transformation has revolutionized the banking industry, ushering in an era of enhanced customer experiences and operational efficiency. The convergence of Internet of Things (IoT) and Artificial Intelligence (AI) technologies has further propelled this evolution by providing real-time insights into customer behavior. This research explores the integration of IoT and AI for real-time customer behavior analysis in the context of digital banking. The proliferation of connected devices, ranging from smart phones to wearables, has generated an unprecedented volume of data. IoT facilitates the collection of diverse data points, such as transaction history, location information, and device interactions, creating a comprehensive digital footprint for each customer. Simultaneously, AI algorithms leverage this wealth of data to analyze, predict, and respond to customer behavior dynamically. In the realm of digital banking, understanding and adapting to customer behavior in real-time is crucial for providing personalized services, preventing fraud, and optimizing operational processes. This research delves into the mechanisms by which IoT sensors and devices, coupled with AI algorithms, enable banks to gain deeper insights into customer behavior patterns. Key components of the proposed system include data acquisition through IoT devices, secure data transmission protocols, and AI-driven analytics engines. In conclusion, this research advocates for the symbiotic relationship between IoT and AI in digital banking to enable real-time customer behavior analysis.  2024 IEEE.</text>
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                <text>Madhumita G., Vels Institute of Science, Technology and Advanced Studies, Department of MBA, Tamil Nadu, Chennai, India; Das T., Christ University, Department of School of Business Management, UP, Ghaziabad, India; Das S., Christ University, Department of School of Commerce, Finance &amp;amp; Accountancy, UP, Ghaziabad, India; Khatri E., Nitte Meenakshi Institute of Technology, Department of Management Studies, Karnataka, Bengaluru, India; Ravisankar P., Saveetha College of Liberal Arts and Sciences, Department of Commerce, Thandalam, Chennai, India; Hemachandu P., Sasi Institute of Technology and Engineering, EEE Department, Andhrapradesh, Tadepallidusem, 534101, India</text>
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                <text>Coloring of n-inordinate invariant intersection graphs</text>
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                <text>Fix of a permutation; Intersection graphs; Invariant intersection graph; n-inordinate invariant intersection graphs; Permutation group</text>
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                <text>In the literature of algebraic graph theory, an algebraic intersection graph called the invariant intersection graph of a graph has been constructed from the automorphism group of a graph. A specific class of these invariant intersection graphs was identified as the n-inordinate invariant intersection graphs, and its structural properties has been studied. In this article, we study the different types of proper vertex coloring schemes of these n-inordinate invariant intersection graphs and their complements, by obtaining the coloring pattern and the chromatic number associated.  2024 The Author(s)</text>
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                <text>Journal of Combinatorial Mathematics and Combinatorial Computing, Vol-123, pp. 369-381.</text>
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                <text>ISSN: 8353026</text>
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                <text>Madhumitha S., Department of Mathematics, Christ University, Bangalore, India; Naduvath S., Department of Mathematics, Christ University, Bangalore, India</text>
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                <text>Graphs on groups in terms of the order of elements: A review</text>
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                <text>Coprime graph; non-coprime graph; order divisor graph; order graph; order prime divisor graph; order product prime graph; order sum graph; order super graph; prime coprime graph</text>
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                <text>Two mathematical fields that concentrate on creating and analyzing structures are algebra and graph theory. There are numerous studies linking algebraic structures like groups, rings, fields and vector spaces with graph theory. Several algebraic graphs have been defined based on the properties of the order of the group and its elements. In this paper, we systematically review the literature on such graphs to understand the research dynamics in the field.  2024 World Scientific Publishing Company.</text>
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                <text>Madhumitha S., Department of Mathematics, CHRIST (Deemed to be University), Karnataka, Bengaluru, 560029, India; Naduvath S., Department of Mathematics, CHRIST (Deemed to be University), Karnataka, Bengaluru, 560029, India</text>
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                <text>The study on graphs emerging from different algebraic structures such as groups, rings, fields, vector spaces, etc. is a prominent area of research in mathematics, as algebra and graph theory are two mathematical fields that focus on creating and analysing structures. There are numerous studies linking algebraic structures and graphs, which began with the introduction of Cayley graphs of groups. Several algebraic graphs have been defined on rings, a fast-growing area in the literature. In this article, we systematically review the literature on some variants of Cayley graphs that are defined on rings and highlight the properties and characteristics of such graphs, to showcase the research in this area.  2023 by the authors.</text>
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                <text>Madhumitha S., Department of Mathematics, CHRIST (Deemed to Be University), Bangalore, 560029, India; Naduvath S., Department of Mathematics, CHRIST (Deemed to Be University), Bangalore, 560029, India</text>
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                <text>Certain variants of domatic partitions of n-inordinate invariant intersection graphs</text>
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                <text>Madhumitha S., Center for Mathematical Needs, Department of Mathematics, Christ University, Karnataka, Bangalore, 560029, India; Naduvath S., Center for Mathematical Needs, Department of Mathematics, Christ University, Karnataka, Bangalore, 560029, India</text>
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                <text>A class of algebraic intersection graphs, called the n-inordinate invariant intersection graphs, are introduced in the literature and several properties of these graphs are being investigated. Domination in graphs is an important structural property and partitioning the vertex set of a graph into dominating sets is called the domatic partition of a graph. In this paper, we analyze the structure of the n-inordinate invariant intersection graphs by investigating certain variants of domatic partitions of these graphs, that are defined based on different types of domination in graphs.  2026 World Scientific Publishing Company.</text>
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                <text>Madhumitha, S.; Naduvath, Sudev</text>
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                <text>A study on the invariant intersection graph of a graph</text>
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                <text>Madhumitha S., Department of Mathematics, Christ University, Bangalore, India; Naduvath S., Department of Mathematics, Christ University, Bangalore, India</text>
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                <text>Analyzing the structure of the automorphism groups of graphs, and investigating the properties of graphs that are constructed from algebraic structures are two important research topics in algebraic graph theory. Blending these two aspects of study, an algebraic intersection graph, called the invariant intersection graph of a graph, has been introduced in the literature. In this paper, we study certain properties of the invariant intersection graphs of graphs, and obtain some structural characterizations of these graphs, based on the automorphism group of the graph on which the invariant intersection graph is constructed.  2026 World Scientific Publishing Company.</text>
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                <text>Coalition partitions of n-inordinate invariant intersection graphs</text>
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                <text>A class of algebraic intersection graphs, called the n-inordinate invariant intersection graphs, has been introduced and various properties of these graphs are investigated in the literature. Domination is an important structural property in graphs and the notion of coalition in graphs has been recently introduced based on different types of domination in graphs. In this article, we analyse the structure of the n-inordinate invariant intersection graphs by investigating certain variants of domination based coalition partitions of them.  2025 World Scientific Publishing Company.</text>
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                <text>Centrality is a real-valued function on the vertex set of a graph that helps in determining the vitality of its vertices. Graph entropy gives the structural information of complex networks, based on some information of the network entities. An algebraic intersection graph called the n-inordinate invariant intersection graph has been constructed from the symmetric group and its structural properties are being studied, in the literature. In this paper, we discuss the centrality measures and the graph entropy of the n-inordinate invariant intersection graphs and their complements, and analyze the sensitivity of these networks, based on the centrality measures of their vertices.  2020 World Scientific Publishing Company.</text>
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                <text>Algebraic graph theory is an intriguing field of research in which various properties of graphs constructed based on algebraic structures are studied. Interlacing two important structural aspects of graphs namely, coloring, and domination in graphs, several domination-related colorings of graphs are introduced in the literature. In this paper, we study such domination-related colorings of algebraic graphs, called the n-inordinate invariant intersection graphs and the n-inordinate invariant non-intersection graphs, that are constructed based on the symmetric group.  2025 World Scientific Publishing Company.</text>
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                <text>Madhumitha S., DEPARTMENT OF MATHEMATICS, CHRIST UNIVERSITY, BANGALORE, India; Naduvath S., DEPARTMENT OF MATHEMATICS, CHRIST UNIVERSITY, BANGALORE, India</text>
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                <text>Coloring and domination in graphs are two well explored areas of research in graph theory. Blending these notions, the dominator coloring of graphs was introduced in the literature; following which several variants of domination related coloring patterns have been defined and studied, based on different types of coloring and domination in graphs. A vertex coloring of a graph that demands the existence of a path in which every internal vertex between two vertices has a unique color is called a rainbow vertex coloring of the graph. In this article, we investigate the rainbow dominator coloring of graphs; a vertex coloring that combines the concepts of rainbow vertex coloring and dominator coloring of graphs. We discuss some properties of the rainbow dominator coloring of graphs and determine the rainbow dominator chromatic number of certain classes of graphs and their complements.  2025, SINUS Association. All rights reserved.</text>
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                <text>Madhumitha S., DEPARTMENT OF MATHEMATICS, CHRIST UNIVERSITY, BANGALORE, India; Naduvath S., DEPARTMENT OF MATHEMATICS, CHRIST UNIVERSITY, BANGALORE, India</text>
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                <text>The concept of dominator coloring of graphs emerged as a combination of the two prominent structural aspects of graphs, namely coloring and domination in graphs. The vertex coloring that demands the existence of a rainbow path between any two vertices of a graph; that is, a path in which every internal vertex has a unique color, is called a rainbow vertex coloring of a graph. Melding the concepts of rainbow vertex coloring and dominator coloring of graphs, the rainbow dominator coloring of graphs has been studied, in the literature. In this article, we investigate the rainbow dominator coloring of some cycle related graphs, and their complements.  2025, SINUS Association. All rights reserved.</text>
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                <text>Invariant intersection graph of a graph</text>
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                <text>Madhumitha S., Department of Mathematics, Christ University, Karnataka, Bangalore, India; Naduvath S., Department of Mathematics, Christ University, Karnataka, Bangalore, India</text>
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                <text>Studies in algebraic graph theory showcase the interplay between group theory and graph theory by defining graphs on groups, investigating their properties, and also by analysing the automorphism groups that emerge from the graphs. In this article, we introduce the idea of constructing an algebraic derived graph; that is, constructing a graph based on the algebraic properties of a graph, by introducing the invariant intersection graph of a graph, constructed based on the automorphism group of a graph. Here, we introduce the graph construction and initiate an investigation on the structure of the invariant intersection graph with respect to the graph and its automorphism group.  2025, Taru Publications. All rights reserved.</text>
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                <text>Automorphism group; Intersection graphs; Invariant intersection graph; Invariant set</text>
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                <text>Color Connections inn-Inordinate Invariant Intersection Graphs</text>
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                <text>Madhumitha S., Department of Mathematics, Christ University, Bangalore, India; Naduvath S., Department of Mathematics, Christ University, Bangalore, India</text>
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                <text>Investigating different properties of algebraic graphs is a curious avenue of research in algebraic graph theory, as these algebraic graphs are well-structured classes of graphs. In these lines, various structural properties of the algebraic intersection graph, called the n-inordinate invariant intersection graphs, have been studied in the literature. Color connections in graphs is the assignment of colors or equivalently, labels to the entities of a non-trivial connected graph, whose protocols are defined based on the connectivity aspects. In this article, we study the different color connections in the n-inordinate invariant intersection graphs and their complements, called the n-inordinate invariant non-intersection graphs.  The Author(s), under exclusive license to Springer Nature Switzerland AG 2026.</text>
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                <text>Improper Injective Coloring Parameters of Certain Cycle-Related Graphs</text>
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                <text>Jordan Journal of Mathematics and Statistics;Volume;18;Issue;4;pp.611-621</text>
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                <text>Madhumitha S., Department of Mathematics, Christ University, Bangalore, India; Pious M., Department of Mathematics, Christ University, Bangalore, India; Naduvath S., Department of Mathematics, Christ University, Bangalore, India</text>
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                <text>Any vertex coloring of a graph can be viewed as a random experiment of assigning colors to the vertices, whose random variable is defined based on the number of vertices assigned a particular color in that coloring. Based on this, the statistical parameters of mean and variance have been extended to chromatic mean and chromatic variance for various vertex colorings of graphs in the literature. In this article, the ideas of chromatic mean and chromatic variance of cycle-related graphs with respect to their improper injective coloring are investigated.  (2025), (Yarmouk University). All rights reserved.</text>
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                <text>chromatic mean; chromatic sum; chromatic variance; Improper coloring; injective coloring</text>
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                <text>Geodetic sets in n-inordinate invariant intersection graphs</text>
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                <text>Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics;Volume;74;Issue;4;pp.723-732</text>
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                <text>&lt;a href="https://doi.org/10.31801/cfsuasmas.1620815" target="_blank" rel="noreferrer noopener"&gt;https://doi.org/10.31801/cfsuasmas.1620815&lt;/a&gt; &lt;br /&gt;&lt;br /&gt;&lt;a href="https://www.scopus.com/pages/publications/105037946266?origin=resultslist" target="_blank" rel="noreferrer noopener"&gt;https://www.scopus.com/pages/publications/105037946266?origin=resultslist&lt;/a&gt;</text>
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              <elementText elementTextId="223860">
                <text>Madhumitha S., Department of Mathematics, Christ University, Bangalore, India; Naduvath S., Department of Mathematics, Christ University, Bangalore, India</text>
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                <text>Algebraic graph theory is a rapidly growing research area in which several graphs based on algebraic structures are introduced and investigated. The algebraic intersection graphs, called the n-inordinate invariant intersection graphs, and the n-inordinate invariant non-intersection graphs, have been constructed on the symmetric group and various properties of these graphs are studied, in the literature. In this article, we analyse the structure of these graphs by examining different types of geodetic sets in them.  2025, Ankara University Faculty of Science. All rights reserved.</text>
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                <text>convexity; distances in graphs; geodesic; Invariant intersection graphs; n-inordinate invariant intersection graphs</text>
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                <text>Numerical study on magnetohydrodynamics micropolar Carreau nanofluid with Brownian motion and thermophoresis effect</text>
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                <text>Finite difference method; Magnetohydrodynamics; Micropolar Carreau nanofluid; Nonlinear thermal radiation, joule heating</text>
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                <text>The current work explores the investigation of the influence of nonlinear thermal radiation on unsteady, magnetohydrodynamics boundary layer flow of micropolar Carreau nanofluid past a stretching sheet. Viscous dissipation, internal heating, Brownian motion, heat source/sink, thermophoresis, chemical reaction, and Joule heating effects are considered in the study. To analyze the model, the governing partial differential equations are rephrased and written in the non-dimensional form with the relevant dimensionless quantities. To obtain the solutions, the nonlinear non-dimensional governing equations are numerically solved using finite difference approximation. The impact of every significant flow parameter on fluid motion, micro-rotation, temperature, concentration, surface drag, heat, and mass transfer rates are presented through plotted graphs and tables. It is noted from the study that the fluid flow and angular motion increase, whereas the temperature declines with higher values of the micropolar constant. Further, it is noticed that thermal distribution is a rising function of radiation parameter, and due to the nonlinear thermal radiation effect, there is an increase of 4.903% in temperature distribution when compared to linear thermal radiation. To support the validity of the solutions, a comparison was made with notable results from the existing literature for the specific case of this study.  2023 Informa UK Limited, trading as Taylor &amp;amp; Francis Group.</text>
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                <text>Madhura K.R.; Babitha</text>
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                <text>International Journal of Modelling and Simulation</text>
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                <text>&lt;a href="https://doi.org/10.1080/02286203.2023.2234240" target="_blank" rel="noreferrer noopener"&gt;https://doi.org/10.1080/02286203.2023.2234240&lt;/a&gt;
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                <text>Madhura K.R., Post Graduate Department of Mathematics, The National College, Karnataka, Bangalore, India, Trans - Disciplinary Research Centre, National Degree College, Florida International University, Basavanagudi, Miami, United States; Babitha, Department of Mathematics, CHRIST (Deemed to Be University), Karnataka, Bengaluru, India</text>
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