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The Number of Shortest Paths in the (n, k)-Star Graphs

  • Conference paper
Combinatorial Optimization and Applications (COCOA 2010)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 6508))

Abstract

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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Cheng, E., Qiu, K., Shen, Z.Z. (2010). The Number of Shortest Paths in the (n, k)-Star Graphs. In: Wu, W., Daescu, O. (eds) Combinatorial Optimization and Applications. COCOA 2010. Lecture Notes in Computer Science, vol 6508. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-17458-2_19

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  • DOI: https://doi.org/10.1007/978-3-642-17458-2_19

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-17457-5

  • Online ISBN: 978-3-642-17458-2

  • eBook Packages: Computer ScienceComputer Science (R0)

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