Weighted and Fuzzy Graph Theory
Series: Studies in Fuzziness and Soft Computing; 429;
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Product details:
- Edition number 2023
- Publisher Springer Nature Switzerland
- Date of Publication 21 August 2024
- Number of Volumes 1 pieces, Book
- ISBN 9783031397585
- Binding Paperback
- See also 9783031397554
- No. of pages216 pages
- Size 235x155 mm
- Language English
- Illustrations XVII, 216 p. 92 illus. Illustrations, black & white 580
Categories
Long description:
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.
Table of Contents:
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.
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