Distance-regular Cayley graphs over ℤ_p^s⊕ℤ_p

2023/08/28 by Zhan, Xiongfeng, Lu, Lu, Huang, Xueyi
#05C25 #05E30 #Combinatorics (math.CO) #FOS: Mathematics

paper · doi:10.48550/arxiv.2308.14368

Abstract

In [Distrance-regular Cayley graphs on dihedral groups, J. Combin. Theory Ser B 97 (2007) 14--33], Miklavič and Potočnik proposed the problem of characterizing distance-regular Cayley graphs, which can be viewed as an extension of the problem of identifying strongly regular Cayley graphs, or equivalently, regular partial difference sets. In this paper, all distance-regular Cayley graphs over ℤ_p^s⊕ℤ_p with p being an odd prime are determined. It is shown that every such graph is isomorphic to a complete graph, a complete multipartite graph, or the line graph of a transversal design TD(r,p) with 2≤ r≤ p-1.

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