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On bipartite distance-regular Cayley graphs with small diameter

van Dam,Edwin R.
; 
Jazaeri,Mojtaba
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 con-structed on the semidirect product of a group — the part of this bipartite Cayley graph which contains the identity element — and Z 2. 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 Miklavič and Potočnik 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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Publisher Copyright: © The authors.
Date
2022-04
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Tilburg University Research Output Collection
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Keywords
RELATIVE DIFFERENCE SETS, CONSTRUCTION, GEOMETRIES
Citation
van Dam, E R & Jazaeri, M 2022, 'On bipartite distance-regular Cayley graphs with small diameter', Electronic Journal of Combinatorics, vol. 29, no. 2, P2.12. https://doi.org/10.37236/10757
URI
https://hdl.handle.net/20.500.14602/77550
License
info:eu-repo/semantics/openAccess
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