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Endomorphisms of Twisted Grassmann Graphs

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Abstract

A graph G is called a pseudo-core if every endomorphism of G is either an automorphism or a colouring. An interesting problem in graph theory is to distinguish whether a graph is a core. The twisted Grassmann graphs, constructed by van Dam and Koolen in (Invent Math 162:189–193, 2005), are the first known family of non-vertex-transitive distance-regular graphs with unbounded diameter. In this paper, we show that every twisted Grassmann graph is a pseudo-core.

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Acknowledgments

The authors are thankful to the anonymous reviewers for many helpful suggestions and great improvements in proofs. This research was supported by National Natural Science Foundation of China (Projects 11371072, 11301270, 11271047, 11371204, 11501036, 11671043), the Fundamental Research Funds for the Central University of China, and Youth Scholar Program of Beijing Normal University and China Postdoctoral Science Foundation (2015M570958).

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Authors and Affiliations

  1. School of Mathematical Sciences, Laboratory of Mathematics and Complex Systems, Beijing Normal University, Beijing, 100875, China

    Benjian Lv & Kaishun Wang

  2. School of Mathematics and Statistics, Changsha University of Science and Technology, Changsha, 410004, China

    Li-Ping Huang

Authors
  1. Benjian Lv
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  2. Li-Ping Huang
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  3. Kaishun Wang
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Correspondence to Benjian Lv.

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Supported by NSFC (Projects 11371072, 11301270, 11271047, 11371204, 11501036, 11671043), the Fundamental Research Funds for the Central University of China, and Youth Scholar Program of Beijing Normal University and China Postdoctoral Science Foundation (2015M570958).

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Lv, B., Huang, LP. & Wang, K. Endomorphisms of Twisted Grassmann Graphs. Graphs and Combinatorics 33, 157–169 (2017). https://doi.org/10.1007/s00373-016-1738-3

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  • DOI: https://doi.org/10.1007/s00373-016-1738-3

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