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- W2164198134 abstract "An essential means to upgrade network reliability is to prepare several substitutable paths between two vertices. We idealize the substitutability in a narrow sense. We will study the mutual relationship between a bundle of shortest paths between any two vertices, and a third vertex from the viewpoint of path multiplicity in case there are some shortest paths between any two vertices. Initially, we will extend a concept of the cutting number, which represents a mutual relationship between a path of any pair of vertices and a third vertex in a tree graph. Then we will generalize it as the intersection function in any graph. Afterward, we will introduce conditions of decreasing this intersection function by inserting edges into the graph. Further, we will demonstrate the main features of this intersection function based upon the conditions. They can provide a new definition of the center in graphs with regard to reliability. We will extend the concept of the intersection function to an edge intersection function." @default.
- W2164198134 created "2016-06-24" @default.
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- W2164198134 date "1980-11-01" @default.
- W2164198134 modified "2023-09-27" @default.
- W2164198134 title "Intersection functions of shortest paths in a nondirected graph" @default.
- W2164198134 cites W2015126386 @default.
- W2164198134 doi "https://doi.org/10.1002/ecja.4410631102" @default.
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