03095nam 22005535 450 991074118900332120230820184817.03-031-39756-810.1007/978-3-031-39756-1(MiAaPQ)EBC30716857(Au-PeEL)EBL30716857(DE-He213)978-3-031-39756-1(PPN)272260525(CKB)28008128100041(EXLCZ)992800812810004120230820d2023 u| 0engurcnu||||||||txtrdacontentcrdamediacrrdacarrierWeighted and Fuzzy Graph Theory /by Sunil Mathew, John N. Mordeson, M. Binu1st ed. 2023.Cham :Springer Nature Switzerland :Imprint: Springer,2023.1 online resource (226 pages)Studies in Fuzziness and Soft Computing,1860-0808 ;429Print version: Mathew, Sunil Weighted and Fuzzy Graph Theory Cham : Springer,c2023 9783031397554 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.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.Studies in Fuzziness and Soft Computing,1860-0808 ;429Computational intelligenceGraph theoryComputational IntelligenceGraph TheoryComputational intelligence.Graph theory.Computational Intelligence.Graph Theory.006.3Mathew Sunil1061654Mordeson John N63000Binu M1424070MiAaPQMiAaPQMiAaPQBOOK9910741189003321Weighted and Fuzzy Graph Theory3552948UNINA