Titlebook: Weighted and Fuzzy Graph Theory; Sunil Mathew,John N. Mordeson,M. Binu Book 2023 The Editor(s) (if applicable) and The Author(s), under ex

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Degree Sequences and Saturation, different weighted graph structures. Due to the scope and wide applications, detailed study and characterizations are carried out in partial trees and partial blocks. Mathematical manipulations at the studies on weighted graphs can be simplified with the help of these sequences. This chapter is bas

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Intervals and Gates,t ., then . is called the central vertex of .. Here . denotes the minimum. Also, . is the radius of . with respect to the metric .. The center of . denoted by . is the subgraph of . induced by the central vertices of . with respect to .. An eccentric vertex of . with respect to . is that vertex . su

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Distance and Convexity,n weighted graphs also. The distance between two vertices in a weighted graph is defined as the minimum of the sum of weights over all geodesics connecting them. This section defines a new kind of distance in 2-connected weighted graphs named as the weighted distance.

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Intervals and Gates,t ., then . is called the central vertex of .. Here . denotes the minimum. Also, . is the radius of . with respect to the metric .. The center of . denoted by . is the subgraph of . induced by the central vertices of . with respect to .. An eccentric vertex of . with respect to . is that vertex . su

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Book 2023depending 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 li

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