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The Number of Shortest Paths in the

The Number of Shortest Paths in the,10.1007/978-3-642-17458-2_19,Eddie Cheng,Ke Qiu,Zhi Zhang Shen

The Number of Shortest Paths in the  
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We enumerate all of the shortest paths between any vertex v and the identity vertex in an (n, k)-star graph by enumerating the minimum factorizations of v in terms of the transpositions corresponding to edges in that graph. This result generalizes a previous one for the star graph, and can be applied to obtain the number of the shortest paths between a pair of vertices in some of the other similar structures. It also implies an algorithm to enumerate all such paths.
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