On edge-transitive dihedrants

Let γ be a Cayley graph over a dihedral group D_2n (a dihedrant for short) and G the group of automorphisms of γ. Suppose G acts transitively on the edges of γ. The problem of characterizing such graphs was proposed by Song et al. It is currently solved only under additional assumptions on γ  or G.

In this talk, we introduce two new infinite families of edge-transitive dihedrants and show that the graph γ is either described in the earlier papers, belongs to one of the two new families, or the group G satisfies certain conditions. Using these conditions, we also classify γ in the case when G is a solvable group. This generalizes a result of Pan et al. dealing with the case where (D_2n)_R is normal in G.

This is a joint work with István Kovács.