Geodesic
On bipartite distance-regular Cayley graphs with small diameter
The electronic journal of combinatorics, Tome 29 (2022) no. 2
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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 $\mathbb{Z}_{2}$. 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.
DOI : 10.37236/10757
Classification : 05C25, 05C12, 05B10
Mots-clés : dihedrant, difference set, symmetric design 
@article{10_37236_10757,
     author = {Edwin R. van Dam and Mojtaba Jazaeri},
     title = {On bipartite distance-regular {Cayley} graphs with small diameter},
     journal = {The electronic journal of combinatorics},
     year = {2022},
     volume = {29},
     number = {2},
     doi = {10.37236/10757},
     zbl = {1487.05126},
     url = {http://geodesic.mathdoc.fr/articles/10.37236/10757/}
}
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Edwin R. van Dam; Mojtaba Jazaeri. On bipartite distance-regular Cayley graphs with small diameter. The electronic journal of combinatorics, Tome 29 (2022) no. 2. doi: 10.37236/10757

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