This book provides an extensive set of tools for applying fuzzy mathematics and graph theory to real-life problems. Balancing the basics and latest developments in fuzzy graph theory, this book starts with existing fundamental theories such as connectivity, isomorphism, products of fuzzy graphs, and different types of paths and arcs in fuzzy graphs to focus on advanced concepts such as planarity in fuzzy graphs, fuzzy competition graphs, fuzzy threshold graphs, fuzzy tolerance graphs, fuzzy trees, coloring in fuzzy graphs, bipolar fuzzy graphs, intuitionistic fuzzy graphs, m-polar fuzzy graphs, applications of fuzzy graphs, and more. Each chapter includes a number of key representative applications of the discussed concept. An authoritative, self-contained, and inspiring read on the theory and modern applications of fuzzy graphs, this book is of value to advanced undergraduate and graduate students of mathematics, engineering, and computer science, as well as researchers interested in new developments in fuzzy logic and applied mathematics.
This book provides an extensive set of tools for applying fuzzy mathematics and graph theory to real-life problems. Balancing the basics and latest developments in fuzzy graph theory, this book starts with existing fundamental theories such as connectivity, isomorphism, products of fuzzy graphs, and different types of paths and arcs in fuzzy graphs to focus on advanced concepts such as planarity in fuzzy graphs, fuzzy competition graphs, fuzzy threshold graphs, fuzzy tolerance graphs, fuzzy trees, coloring in fuzzy graphs, bipolar fuzzy graphs, intuitionistic fuzzy graphs, m-polar fuzzy graphs, applications of fuzzy graphs, and more. Each chapter includes a number of key representative applications of the discussed concept. An authoritative, self-contained, and inspiring read on the theory and modern applications of fuzzy graphs, this book is of value to advanced undergraduate and graduate students of mathematics, engineering, and computer science, as well as researchers interested in new developments in fuzzy logic and applied mathematics.
Apabhramsa forms the previous stage of modern Indo-Aryan languages like Hindi, Gujarati, Marathi, Bengali etc., its study is essential not only for its literature but also for the formation of modern Indian languages. The present volume is a chrono-regional study of nearly all the edited Apabhramsa texts available. The Apabhramsa texts were classified according to the place of their composition and the linguistic data was arranged in a chronological sequence and thus the space-time context of each forms was determined. After illuminating the term Apabhramsa and fixing its period and classifying the texts in their space-time context, the author offers a general conspectus of the phonological and morphological features of Apabhramsa in the Introduction. Then follow sections on Phonology, Declension, Conjugation, Nominal Stem-formation according to diachronic method connecting the evolved linguistic features to its modern descendant wherever possible. The work ends with an Index Verborum which lists all the words occurring in the study with their Sanskrit and Prakrit etymologies as well as references to their cognates in the modern Indo-Aryan. As Dr. Siddheshwar Varma says, ''It is the history of Indo-Aryan between A.D. 500-1200.
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