István Kovács (FAMNIT UP, Slovenija): G-arc-regular dihedrants

Povzetek: In the talk we consider the following situation: X is a connected, G-arc-regular graph of order 2n, D \le G is a regular dihedral subgroup such that its unique cyclic subgroup is core-free in G. It will be shown that one of the following holds: (i) n=1, X=K_2, and G=S_2, (ii) n=2, X=K_4, and G=A_4, (iii) n=3, X=K_{2,2,2}, and G=S_4, (iv) n=2m, m is an odd number, X=K_{n,n}, and G=(D_n \times D_n) \rtimes Z_2.