For Artin groups of dihedral type, we compute the Bredon homology classifying space for family virtually cyclic subgroups with coefficients in K-theory a group ring.

The main result of this article is a classification of distance-regular Cayley graphs on dihedral groups. There exist four obvious families of such graphs, which are called trivial. These are: complete graphs, complete bipartite graphs, complete bipartite graphs with the edges of a 1-factor removed, and cycles. It is proved that every nontrivial distance-regular Cayley graph on a dihedral group...

We examine two particular constructions that derive from a 2-group G = G(·) another 2-group G(∗) for the case when G(·) is one of D2n , SD2n , Q2n . The constructions (the cyclic one and the dihedral one) have the property that x ∗ y = x · y for exactly 3/4 of all pairs (x, y) ∈ G × G. If G(◦) and G(∗) are such 2-groups that x ◦ y 6= x ∗ y for less then a quarter of all pairs (x, y) ∈ G × G, th...