2025/03/14 by Yang, Jun-Feng, Feng, Yan-Quan, Yin, Fu-Gang +1
#05C25 #20B25 #Combinatorics (math.CO) #FOS: Mathematics #Group Theory (math.GR)
paper · doi:10.48550/arxiv.2503.10994
A Cayley digraph on a group G is called NNN if the Cayley digraph is normal and its automorphism group contains a non-normal regular subgroup isomorphic to G. A group is called NNND-group or NNN-group if there is an NNN Cayley digraph or graph on the group, respectively. In this paper, it is shown that there is no cyclic NNND-group, and hence no cyclic NNN-group. Furthermore, a dihedral group of order 2n is an NNND-group or an NNN-group if and only if n≥ 6 is even and n\not=8.