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Combinatorial Properties of Full-Flag Johnson Graphs

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Combinatorial Algorithms (IWOCA 2015)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 9538))

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Abstract

The Johnson graphs J(n, k) are a well-known family of combinatorial graphs whose applications and generalizations have been studied extensively in the literature. In this paper, we present a new variant of the family of Johnson graphs, the Full-Flag Johnson graphs, and discuss their combinatorial properties. We show that the Full-Flag Johnson graphs are Cayley graphs on \(S_n\) generated by certain well-known classes of permutations and that they are in fact generalizations of permutahedra. Our main result will be to establish a tight \(\varTheta (n^2/k^2)\) bound for the diameter of the Full-Flag Johnson graph FJ(n, k).

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Author information

Authors and Affiliations

  1. Department of Mathematics, Princeton University, Princeton, NJ, 08544, USA

    Irving Dai

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  1. Irving Dai
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Correspondence to Irving Dai .

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Editors and Affiliations

  1. Dept. of Computer Science, University of Verona, Verona, Italy

    Zsuzsanna Lipták

  2. Dept. of Computing and Software, McMaster University, Hamilton, Canada

    William F. Smyth

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Dai, I. (2016). Combinatorial Properties of Full-Flag Johnson Graphs. In: Lipták, Z., Smyth, W. (eds) Combinatorial Algorithms. IWOCA 2015. Lecture Notes in Computer Science(), vol 9538. Springer, Cham. https://doi.org/10.1007/978-3-319-29516-9_10

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  • DOI: https://doi.org/10.1007/978-3-319-29516-9_10

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-29515-2

  • Online ISBN: 978-3-319-29516-9

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