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Graph Theory and Decomposition
The book Graph Theory and Decomposition covers major areas of the decomposition of graphs. It is a three-part reference book with nine chapters that is aimed at enthusiasts as well as research scholars. It comprehends historical evolution and basic terminologies, and it deliberates on decompositions into cyclic graphs, such as cycle, digraph, and K4-e decompositions. In addition to determining the pendant number of graphs, it has a discourse on decomposing a graph into acyclic graphs like general tree, path, and star decompositions. It summarises another recently developed decomposition technique, which decomposes the given graph into multiple types of subgraphs. Major conjectures on graph decompositions are elaborately discussed. It alludes to a comprehensive bibliography that includes over 500 monographs and journal articles. It includes more than 500 theorems, around 100 definitions, 56 conjectures, 40 open problems, and an algorithm. The index section facilitates easy access to definitions, major conjectures, and named theorems. Thus, the book Graph Theory and Decomposition will be a great asset, we hope, in the field of decompositions of graphs and will serve as a reference book for all who are passionate about graph theory. 2024 Jomon Kottarathil, Sudev Naduvath and Joseph Varghese Kureethara. -
Graph Theory in Computer Science
This book is a vital resource for anyone looking to understand the essential role of graph theory as the unifying thread that connects and provides innovative solutions across a wide spectrum of modern computer science disciplines. Graph theory is a traditional mathematical discipline that has evolved as a basic tool for modeling and analyzing the complex relationships between different technological landscapes. Graph theory helps explain the semantic and syntactic relationships in natural language processing, a technology behind many businesses. Disciplinary and industry developments are seeing a major transition towards more interconnected and data-driven decision-making, and the application of graph theory will facilitate this transition. Disciplines such as parallel and distributive computing will gain insights into how graph theory can help with resource optimization and job scheduling, creating considerable change in the design and development of scalable systems. This book provides comprehensive coverage of how graph theory acts as the thread that connects different areas of computer science to create innovative solutions to modern technological problems. Using a multi-faceted approach, the book explores the fundamentals and role of graph theory in molding complex computational processes across a wide spectrum of computer science. 2026 Scrivener Publishing LLC. -
Graph theory in security, utility, aesthetics and affordability
The theory of Domination in graphs is used in security systems. Landscaping uses planarity and crossing number. In layout designs, hamiltoincity is regulalry used. Edge-weighted graphs and Max-Flow Min-Cut models are also discussed in this paper. 2023 Author(s). -
GraphDrift-net: a dynamic graph-based framework for concept drift detection in short unstructured text streams
Detecting concept drift in text streams is challenging due to the rapid evolution of language, shifting user behavior, and temporal dependencies. Issues like data sparsity, high dimensionality, lack of labeled data, and multimodal drift further complicate real-time detection and adaptation. This paper proposes GraphDrift-net, a novel dynamic graph-based framework for detecting and adapting to concept drift in evolving text streams. The model comprise of the following components: evolving Time BERT (EvoTimeBERT), which captures temporal language evolution via historical token memory and multi-scale temporal convolutions, hierarchical temporal graph network with dynamic topics and adaptive memory (HTGN-DTAM), a heterogeneous graph neural network that dynamically constructs topic-aware graphs to track changing semantics and Chronograph Detection, a time-series-based drift detection method leveraging graph statistics such as node centrality and clustering coefficient changes. In addition, graph neural reinforcement learning framework (GNRL), a reinforcement learning-based adaptive learning module, enables model adaptability by word embedding update, memory decay rate tuning, and few-shot adaptation. Experimental evaluations over various real-world datasets, including Twitter-1, Twitter-2, Enron, and News20, demonstrate that GraphDrift-net outperforms other methods in accuracy, F1-score, and drift detection sensitivity. The model achieves accuracy as high as 99.7%, is able to identify more drift points, and is more stable with computational efficiency, making it extremely appropriate for real-time text stream applications. The Author(s), under exclusive licence to SocietItaliana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature 2025. -
Graphene and graphene enhanced nanomaterials from biological precursors synthesis characterization and proliferant applications
Graphene family materials with non-photocatalytic biocidal properties are highly sought after in the field of biomedicine and nanobiotechnology. But the applications of graphene-based materials were often hampered by their high production cost, low yield, non-renewable precursors, harmful processing newlinetechniques, etc. In this context, this study presented the successful usage of biomass materials as sustainable feedstock for the production of graphene derivatives. Five raw materials of biological origin namely, coconut shell, wood, sugarcane bagasse, Colocasia esculenta leaves and Nelumbo nucifera leaves, were investigated. The graphitized forms of the above materials were newlineused as precursors for the graphene nanomaterial synthesis. They were chemically oxidized and functionalized with tin oxide nanoparticles to form the composite. Nano-systems obtained using an identical chemical route from a universal source of carbon nanomaterials, namely carbon black, were also newlinestudied for the purpose of validation and comparison. The synthesis protocols adopted for the preparation of graphene-based materials were devoid of hazardous reducing agents or byproducts. The products obtained after each stage of treatment were characterized with the help of various spectroscopic and microscopic techniques. newlineEven though structural properties of all the precursors appeared to be broadly the same, a variation in their morphology and defect density was discerned. Various analyses revealed the formation of graphene oxide domains with distinct dimensions after the oxidative treatment. An increase in defect newlinedensity was also observed due to the intercalation of oxygen groups to the carbon layers. Post composite formation, a distribution of ultrafine tin oxide newlinenanoparticles on the graphene surface was observed. The distribution of oxygen newlinefunctionalities on the carbon backbone were found to play a major role in governing the dispersal of tin oxide particles during the nanocomposite formation. -
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Graphene doped spray dried ceramic nano oxides for high capacity battery electrodes
Electric vehicles or portable electronic devices have come to rely heavily upon electrochemical devices, such as rechargeable batteries with optimum charge discharge characteristics, current ratings, charge-discharge rate (rate capability), cyclability etc. to perform under the expected service conditions. One of the goals of a rechargeable battery materials researcher is to fabricate materials to realize solid-state batteries with high reliability and lithium-air batteries with ultimate capacities. Most of the materials although possess high theoretical energy density values: invariably suffer from inferior cyclic performance. The performance of these batteries is guided by the electrodes within these devices which in turn depend upon the materials used to fabricate them. Chemical composition and its uniformity, consistency in microstructural features, and adequate choice of various layers that may be in the form of coatings to be overlaid on the base materials mostly comprised of ceramic oxides such as oxides of Li doped with niobates, manganates, vanadate etc. with carbon or graphene coated over layers to provide with the suitable interfacial conductivity as electrode materials in Li-ion batteries. The interfacial layers and the mechanism of interfacial phenomena encompassing the grains play a significant role in determining the performance. Optimum microstructure is obtained by choosing the right processing equipment and spray drying the composition in slurry form provides the most optimum solution. Further, spray drying offers high potential for a transfer from a lab scale technology to industrial level extrapolation. In this paper, nano graphene has been spray dried along with nano alumina grains in water media and polyvinyl alcohol binder to ascertain the free flowability, consistency in formation of graphene over layer on alumina grains as well as uniformity in graphene on alumina composition. The free flowing spray dried graphene coated alumina powders were analysed via SEM, EDS and XRD and results are presented. Additional information based on a review conducted on published information on most popular compositions in terms of electrode materials such as in Li-ion, sodium-ion etc have also been included. In the review section the rapidly increasing literature on spray drying of solutions and suspensions are also included. Published under licence by IOP Publishing Ltd. -
Graphene Nanotechnology for Renewable Energy Systems
The high degree of mechanical, electrical, and thermal conductivity of graphene enables its application in the renewable energy sector. Graphene plays a vital role in diodes, photovoltaic cells, supercapacitors, batteries, and full cells applications and it enhances the existing efficiency in a tremendous way. The addition of graphene can do tremendous effects on all kinds of inorganic and organic materials for solar cells. In the supercapacitor domain, graphene plays a vital role to provide a large surface which can be useful for energy storage applications. The hybrid supercapacitor and battery trends in research and technology have been discussed. The electrical vehicles and green applications need and accomplishments of graphene and its derivatives have also been described. 2023, The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. -
Graphene quantum dots: Promising catalysts for electrocatalytic water splitting
In recent times, graphene quantum dots have attracted attention from both academia and industry due to their low cost, non-toxicity, abundance, inertness, stability, photoluminescence, and ease of functionalization. Graphene quantum dots are doped with heteroatoms and modified structurally with metals/metal oxides to form composites that find immense application in catalysis. Electrocatalytic water splitting is an energy efficient route for oxygen evolution, hydrogen evolution, and oxygen reduction reactions. Graphene quantum dots based composites have been extensively employed for electrocatalytic water splitting applications, with remarkable results. This chapter focuses on electrocatalytic applications of modified graphene quantum dots in water splitting. 2024 Nova Science Publishers, Inc. All rights reserved. -
Graphene-based nanocomposites for energy conversion and storage
Graphene, consisting of a single layer of carbon atoms organized in a hexagonal pattern, exhibits exceptional electrical, mechanical, and thermal characteristics. The combined effects arising from the synergy of graphene with other materials assume a pivotal role in enhancing the overall performance of energy devices. The initial section of this chapter focuses on the utilization of graphene composites in energy conversion technologies, spanning solar cells, water-splitting devices, and fuel cells. Subsequently, this chapter explores the application of graphene composites in energy storage systems such as lithium-ion batteries and supercapacitors. Graphene provides a significant surface area, facilitates rapid electron transport, and offers mechanical stability, all positively impacting the energy storage capacity and cyclic stability of these devices. Furthermore, the chapter discusses the current research trends, challenges, and future prospects concerning graphene composites for energy conversion and storage applications. 2025 Elsevier Inc. All rights reserved. -
Graphene-metal oxide composite materials for supercapacitor applications
Recently, supercapacitors have emerged as one of the potential candidates for electrochemical energy storage applications owing to their excellent capacity properties, high power density, appreciable cyclic stability, and environmentally benign nature. Graphene has paved the way as a supercapacitor electrode because of its exceptional attributes, including its conductivity, and mechanical and electrical properties. The efficiency of supercapacitors has been significantly impeded by the aggregation of graphene layers brought on by the considerable van der Waals attractions. Numerous methods have been developed to get over the limitations and make graphene a prime choice for supercapacitors. It is anticipated that combining graphene with metal oxides will improve its capacitive properties due to the mutual contribution of the individual components. In this chapter, various synthetic methods for graphene-metal oxide-based binary and ternary composites, as well as their application as supercapacitor electrodes, are explained in detail. The current research directions and future scope of graphene-metal oxide-based composites for supercapacitor application are also included. The Royal Society of Chemistry 2025. -
Graphene-metal oxide composites for electrochemical energy storage and conversion
The development of clean and renewable alternative energy sources is essential due to the rising energy consumption. Advancements in energy conversion and storage technologies, such as fuel cells, batteries, and solar cells, are currently the subject of active research. The unique structure and properties of two-dimensional graphene materials are explored in developing energy devices. The efficient utilization of graphene's enormous specific surface area and exceptional electrical, chemical, and mechanical properties still remains a challenge to researchers due to the agglomeration of its layers. The introduction of metal oxides into these 2D layers helps to enhance their structural and electrochemical stability, which helps in the production of energy storage devices. This chapter discusses the synthesis protocols, tunable properties, as a function of size and shape, and characterization tools. It also provides a deeper understanding of graphene-metal oxide composites in various energy storage devices, highlighting the importance of the synergistic effects between graphene and metal oxides. The chapter concludes with the prospects and potential of graphene-metal oxide composites for energy storage applications. The Royal Society of Chemistry 2025. -
GrapheneLiquid Crystal Synergy: Advancing Sensor Technologies across Multiple Domains
This review explores the integration of graphene and liquid crystals to advance sensor technologies across multiple domains, with a focus on recent developments in thermal and infrared sensing, flexible actuators, chemical and biological detection, and environmental monitoring systems. The synergy between graphenes exceptional electrical, optical, and thermal properties and the dynamic behavior of liquid crystals leads to sensors with significantly enhanced sensitivity, selectivity, and versatility. Notable contributions of this review include highlighting key advancements such as graphene-doped liquid crystal IR detectors, shape-memory polymers for flexible actuators, and composite hydrogels for environmental pollutant detection. Additionally, this review addresses ongoing challenges in scalability and integration, providing insights into current research efforts aimed at overcoming these obstacles. The potential for multi-modal sensing, self-powered devices, and AI integration is discussed, suggesting a transformative impact of these composite sensors on various sectors, including health, environmental monitoring, and technology. This review demonstrates how the fusion of graphene and liquid crystals is pushing the boundaries of sensor technology, offering more sensitive, adaptable, and innovative solutions to global challenges. 2024 by the authors. -
Graphitic carbon nitride (GCN) for solar cell applications
There is an eminent global energy crisis and photovoltaics as one of the primary renewable energy sources is playing an important part in offsetting the dependency on fossil fuels. Current solar cells technology is dominated by silicon, and researchers are trying to replace it with organic and nanocrystalline semiconducting materials. Graphitic carbon nitride (g-C3N4, GCN) has gained interest as a visible light driven photocatalyst with a unique 2D structure, excellent chemical stability and tunable electronic structure along with attractive optoelectronic properties. Pure GCN suffers from low surface area and rapid recombination of photo-generated electron-hole pairs resulting in low photovoltaic and photocatalytic activity and hence modification by doping with other atoms is required. Photocatalytic applications of GCN based nanomaterials for water splitting, hydrogen production, CO2 reduction and pollutant degradation has been extensively investigated and systematically reviewed. However, their applications as energy storage has been explored recently and there is a lack of comprehensive review that systematically summarizes the application of GCN and GCN-based heterostructures for solar cell applications. Heterojunctions with superior light absorption and appropriate conduction band and valence band alignment is a promising approach for the applications in efficient environmental remediation and solar energy storage. This critical review summarizes the synthesis and advances of GCN nanocomposites modified with semiconductors (TiO2, ZnO), bismuth titanate, strontium titanate and rare earth metals for solar cell applications. GCN-based heterostructures with perovskite and polymer based materials are also presented. The characteristics and transfer mechanism within the various heterojunctions is also reviewed and presented. The review ends with a summary and some perspectives on the challenges and new directions in exploring GCN-based advanced nanomaterials particularly towards photovoltaics and energy storage applications. 2022 Elsevier Inc. All rights reserved. -
Graphitization of coal by bio-solubilization: Structure probe by Raman spectroscopy
Raman spectra of two coal samples of different rank have been examined with Raman spectrometer operating at an excitation wavelength of 514.5 nm. Raman studies manifested the presence of G band conforming the first order scattering of E2g mode. The sp3 domains at about 1355 cm-1 (D band) is an evidence to edge planes and disordered structures. Analysis by curve fitting the first order spectrum justified the presence of G, D1, D2, D3 and D4 bands. The integrated intensity ratio IG/ID? is found to be 3.66 and 5.8 while the ID/ID? ratio is estimated to be about 3 and 4.9 for bituminous and sub-bituminous coal, respectively indicating on-site and hopping defect in the graphene layers. The 2D band is fitted with multiple Lorentian profile has 4 peaks, the intense G?, G?, D + D? and 2D? band at 2445, 2690, 2925 and 3160 cm-1. From the second order spectrum, formation of about 6-8 stacked graphene layers is observed in sub-bitumionus coal. -
Graphs Defined on Rings: A Review
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. -
Graphs Emerging from Finite Dimensional Vector Spaces
A vector space over a field is defined as a collection closed under finite vector addition and scalar multiplication. Over the course of time, researchers have delved into exploring the intricate relationships between existing algebraic structures and graphs. This exploration led to the emergence of a distinctive class of graphs derived from vector spaces, following investigations into graphs originating from groups and rings. This thesis undertakes a thorough examination of a well-established algebraic structure known as the non-zero component graph of a finite-dimensional vector space over finite fields. Expanding on this, the thesis introduces the concept of orthogonal component graphs over finitedimensional vector spaces with a particular emphasis on the field Zp. The non-zero component graph of a finite-dimensional vector space over a newlinefinite field is a graph where vertices represent all possible non-zero vectors in newlinethe vector space. Vertices in the graph are made adjacent if they share a common basis vector in their linear combination. The thesis explores a variety of properties relating to distances, domination, and connectivity. Furthermore, it conducts in-depth study of coloring, color connections, topological indices, and centrality-based sensitivity specifically for non-zero component graphs. The concept of orthogonality among vectors in the vector space paves the way for a novel algebraic graph structure the orthogonal component graph. In this graph, vertices represent all possible non-zero vectors in the vector space, and adjacent vertices correspond to orthogonal vectors. The study extends to determining the properties of the orthogonal component graph, particularly in the newlinecontext of the field Z p. Additionally, it characterises the relationship between newlinenon-zero component graphs and orthogonal component graphs. In the latter chapters, the concept of non-zero component signed graphs is introduced and thoroughly discussed. -
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Graphs on groups in terms of the order of elements: A review
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. -
Graphs with large diameter and their two distance forcing number
For a given simple graph G = (V,E), the two distance forcing number Z2d (G) is defined as the minimum cardinality among all Z2d-sets in G. This paper examine about Z2d (G) of some graphs with large diameter. Also we determine the 2-distance forcing number of some complement graphs. 2021 the author(s).