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Paper   IPM / M / 16991
School of Mathematics
  Title:   On bipartite distance-regular Cayley graphs with small diameter
  Author(s):  Mojtaba Jazaei (Joint with E. R. van Dam)
  Status:   Published
  Journal: Electron. J. Combin.
  Vol.:  29
  Year:  2022
  Pages:   P2.12
  Supported by:  IPM
  Abstract:
We study bipartite distance-regular Cayley graphs with diameter three or four. We give sufficient conditions under which a bipartite Cayley graph can be constructed on the semidirect product of a group - the part of this bipartite Cayley graph which contains the identity element - and Z2. We apply this to the case of bipartite distance-regular Cayley graphs with diameter three, and consider cases where the sufficient conditions are not satisfied for some specific groups such as the dihedral group. We also extend a result by Miklavic and Potocnik that relates difference sets to bipartite distance-regular Cayley graphs with diameter three to the case of diameter four. This new case involves certain partial geometric difference sets and - in the antipodal case - relative difference sets.

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