Weighted and Fuzzy Graph Theory

One of the most preeminent ways of applying mathematics in real-world scenario modeling involves graph theory. A graph can be undirected or directed depending on whether the pairwise relationships among objects are symmetric or not. Nevertheless, in many real-world situations, representing a set of complex relational objects as directed or undirected is not su¢ cient. Weighted graphs o§er a framework that helps to over come certain conceptual limitations. We show using the concept of an isomorphism that weighted graphs have a natural connection to fuzzy graphs. As we show in the book, this allows results to be carried back and forth between weighted graphs and fuzzy graphs. This idea is in keeping with the important paper by Klement and Mesiar that shows that many families of fuzzy sets are lattice isomorphic to each other. We also outline the important work of Head and Weinberger that show how results from ordinary mathematics can be carried over to fuzzy mathematics. We focus on the concepts connectivity, degree sequences and saturation, and intervals and gates in weighted graphs.

The first book written solely on weighted graphs A timely introduction to Weighted and Fuzzy Graph Theory Some of the chapters are written exclusively for weighted graphs and weighted adaptations of fuzzy graph findings

Autorentext

Dr. John N. Mordeson is Professor Emeritus of Mathematics at Creighton University. He received his B.S., M.S., and Ph.D. from Iowa State University. He is a member of Phi Kappa Phi. He has published 19 books and over 200 journal articles, and is on the editorial board of numerous journals. He has served as an external examiner for Ph.D. candidates from India, South Africa, Bulgaria and Pakistan, and has also served as a referee for numerous journals and grant agencies. He is particularly interested in applying mathematics of uncertainty to combat the problem of human träcking. Dr. Sunil Mathew is a faculty member at the Department of Mathematics, NIT Calicut, India. He has holds a master's degree from St. Josephs College, Calicut, and a Ph.D. in Fuzzy Graph Theory from the National Institute of Technology Calicut. He has 20 years of teaching and research experience, and his current research focuses on fuzzy graph theory, bio-computational modeling, graph theory, fractal geometry, and chaos. He has published more than 100 research papers and written ve books, and is an editor and reviewer for several international journals. He is a member of numerous academic bodies and associations.

Inhalt

Graphs and Weighted Graphs.- Connectivity.- More on Connectivity.- Cycle Connectivity.- Distance and Convexity.- Degree Sequences and Saturation.- Intervals and Gates.- Weighted Graphs and Fuzzy Graphs.- Fuzzy Results from Crisp Results.