### ON THE PARTIAL DIFFERENCE SETS IN CAYLEY DERANGEMENT GRAPHS

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#### Abstract

Let $G$ be a finite group. The set $D\subseteq G$

with $|D|=k$ is called a $(n,k,\lambda,\mu)$-partial difference set

(PDS) in $G$ if the differences $d_1d_2 ^{-1}, d_2,d_2\in D, d_1\neq d_2$, represent each non-identity element in $D$ exactly $\lambda$ times and each non-identity element in $G-\{D\}$ exactly $\mu$ times.

In the present paper, we determine for which group $G\in \{D_{2n},T_{4n},U_{6n},V_{8n}\}$ the derangement set is a PDS. We also prove that the derangement set of a Frobenius group is a PDS.

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DOI: https://doi.org/10.22190/FUMI1904651G

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