Advanced Fractal Graph Theory and Applications

This book explores the dynamic interplay between fractals and graph theory, two powerful mathematical tools with vast applications. It presents a strategic combination and the synergistic use of these disciplines to address real-world problems and challenges. The book begins with an introduction to the basic concepts of fractals and graph theory and goes on to explore the applications in various domains, including natural phenomena modeling, scheduling, and network optimisation. This book: Illustrates the innovative ways fractals and graph theory can be combined, laying the groundwork for future applications across various industries Introduces the fundamental concepts and principles of both fractals and graph theory in detail, making it accessible to a broad audience, including those new to these topics Explores practical applications in image processing, network optimisation, social network analysis, and more, demonstrating the real-world impact of these mathematical tools Analyses advanced techniques in graph theory, such as matching, domination, and colouring, with practical examples and case studies Highlights the latest research advancements in fractal graph theory, showcasing its potential for future developments and applications This book is for students, researchers, and professionals in mathematics, computer science, engineering, and related fields.

Table of Contents:
1. Graph Theory- Overview 2. Fractal Graph Theory 3. Fractal & Fractal Geometry 4. Classical Iterated Function Systems 5. Fractals from Iterated Function Systems 6. Application of Fractals in Various Fields 7. Matching and Application of Matching in Real life 8. Domination and its Application in Real Life 9. Coloring and Application of Coloring in Real Life 10. Fractals in medicine 11. Fractals in Circuit Theory 12. Fractals in Architecture 13. Fractal Networks and Deep Learning

About the Author :
1. Dr. P. Tharaniya: In 2022, Dr. P.Tharaniya obtained her Ph.D. in the Department of Mathematics from VELS Institute of Science, Technology and Advanced Studies, Chennai. Currently, she is working as an Assistant Professor in the Department of Mathematics at Rajalakshmi Institute of Technology, Chennai. She has over 14 years of teaching and more than 5 years of Research experience. She has presented at more than 10 International and National Conferences. She has attended many webinars, Faculty Development Programs, and Workshops related to Graph Theory. 12 technical papers published in Journals and Conferences. Fractal Graph Theory, Matching, Domination, and Coloring are some of her research interests. Orcid id: https://orcid.org/0000-0003-2345-7129 Academic url: https://ritchennai.org/index.php ResearchGate : https://www.researchgate.net/profile/P-Tharaniya GoogleScholar: https://scholar.google.com/citations?user=V1xP15gAAAAJ&hl=en&oi=ao 2. Dr.G.Jayalalitha In 2011, Dr.G.Jayalalitha obtained her Ph.D. in Mathematics from Sri Chandrasekharendra Saraswathi Vishwa Mahavidyalaya. She is the lifetime member of the Indian Mathematical Society, MISTE, and The Association of Mathematics Teachers of India. Currently, she is working as a Professor of the Department of Mathematics at VELS Institute of Science, Technology, and Advanced Studies, Chennai. Her teaching and research experience is nearly 18 years. She has published nearly 120 articles and produced 11 Ph.D. Scholars. She has presented at more than 10 International and National Conferences and is also Resource Person, Keynote Speaker in more than 10 programs, and Advisory Board Member in VISTAS. Her papers are cited in nearly 158 and her h-index is 7. Her research interests in Fractals, Mathematical Modelling, Operation Research, and Graph Theory. ORCID ID: https://orcid.org/0000-0002-3247-4697 Scopus ID: http://www.scopus.com/authid/detail.url?authorId=57202163730 Google Scholar Id: http://scholar.google.co.in/citations?user=26pS628AAAAJ ResearchGate: https://www.webofscience.com/wos/author/rid/ABA-8428-2022 3. Pethuru Raj, PhD Vice President and Chief Architect Edge AI Division, Reliance Jio Platforms Ltd. Bangalore, India 560103 Currently working at Reliance Jio Platforms Ltd. (JPL) Bangalore. Previously, worked in IBM Global Cloud Center of Excellence (CoE), Wipro consulting services (WCS), and Robert Bosch Corporate Research (CR). He has gained over 22 years of IT industry experience and eight years of research experience. Finished the CSIR-sponsored PhD degree at Anna University, Chennai, and continued with the UGC-sponsored postdoctoral research in the Department of Computer Science and Automation, Indian Institute of Science (IISc), Bangalore. After that, he was granted two international research fellowships (JSPS and JST) to work as a research scientist for 3.5 years in two leading Japanese universities. He has been an ACM and IEEE professional member. Focuses on some of the digital transformation technologies such as the Internet of Things (IoT), Artificial Intelligence (AI), Streaming Data Analytics, Blockchain, Digital Twins, Cloud-native computing, Edge and Serverless computing, Reliability engineering, Microservices architecture (MSA), Event-driven architecture (EDA), 5G/6G, etc. Technology Books: https://peterindia.net/MyBooks.html Google Scholar: https://scholar.google.co.in/citations?user=yaDflpYAAAAJ&hl=en LinkedIn: https://www.linkedin.com/in/sweetypeter/ 4. B. Sundaravadivazhagan Ph.D, SMIEEE Department of Information Technology University of Technology and Applied Sciences-Al Mussanah, Oman B. Sundaravadivazhagan has obtained PhD in computer science from Anna University, Chennai India. Currently, he is faculty in the Department of Information Technology at the University of Technology, and Applied Science-AL Mussanah in Oman.He has professional memberships in ISACA and ISTE and is a senior member of IEEE.His academic and research background spans more than 23 years at many institutions. Working on two financed research projects for the Ministry of Higher Education Research Innovation in Oman via TRC. His research interests include the Cyber Security, Artificial Intelligence and machine learning, deep learning, and cloud computing. He has published more than 75technical articles in journals and conferences throughout the world. Orcid Id : https://orcid.org/my-orcid?orcid=0000-0002-5515-5769 Academic URL : https://www.act.edu.om/staffdirectory/index.aspx?XY=496 LinkedIn : https://www.linkedin.com/in/dr-b-sundaravadivazhagan-a3562b136/ Google Scholar: https://scholar.google.com/citations?user=gWbzTjMAAAAJ&hl=en