Hypergroups derived from random walks on some infinite graphs

  • Tomohiro Ikkai
  • Yusuke SawadaEmail author


Wildberger gave a method to construct a finite hermitian discrete hypergroup from a random walk on a certain kind of finite graphs. In this article, we reveal that his method is applicable to a random walk on certain kinds of infinite graphs. Moreover, we make some observations of finite or infinite graphs on which a random walk produces a hermitian discrete hypergroup.


Hermitian discrete hypergroups Distance-regular graphs Association schemes Cayley graphs Infinite graphs 

Mathematics Subject Classification

Primary 43A62 Secondary 05C81 



The author expresses his gratitude to Prof. Satoshi Kawakami, Prof. Kohji Matsumoto, Prof. Tatsuya Tsurii, Prof. Shigeru Yamagami and Mr. Ippei Mimura for helpful comments.


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Copyright information

© Springer-Verlag GmbH Austria, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Graduate School of MathematicsNagoya UniversityNagoyaJapan

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