A k-graph \(\mathcal {G}\) is asymmetric if there does not exist an automorphism on \(\mathcal {G}\) other than the identity, and \(\mathcal {G}\) is called minimal asymmetric if it is asymmetric but every non-trivial induced sub-hypergraph of \(\mathcal {G}\) is non-asymmetric. Extending a result of Jiang and Nešetřil (J Comb Theory Ser B 164: 105–118, 2024), we show that for every \(k\ge 3\) , there exist infinitely many minimal asymmetric k-graphs which have maximum degree 2 and are linear. Further, we show that there are infinitely many 2-regular asymmetric k-graphs for \(k\ge 3\) .
