A graph X is said to be G-arc-regular if a subgroup G (= Aut(X) acts regularly on the arcs of X. In this paper connected G-arc-regular graphs are classified in the case when G contains a regular dihedral subgroup D_{2n} of order 2n whose cyclic subgroup C_n (= D_{2n} of index 2 is core-free in G. As an application, all regular Cayley maps over dihedral groups D_{2n}, n odd, are classified.

COBISS.SI-ID: 1024473940

Let G be a finite group with identity element 1, and S be a subset of G such that 1 \notin S and S = S^{−1}. The Cayley graph Cay(G, S) has vertex set G, and x, y in G are adjacent in Cay(G,S) if and only if xy^{−1} is in S. In this paper connected, arc-transitive Cayley graphs Cay(D_{2p^n},S), where D_{2p^n} is the dihedral group of order 2p^n and p is an odd prime, are classified.

COBISS.SI-ID: 1024407124

In this paper a new class of graphs, called quasi m-Cayley graphs, having good symmetry properties, in the sense that they admit a group of automorphisms G that fixes a vertex of the graph and acts semiregularly on the other vertices, is introduced. We determine when these graphs are strongly regular.

COBISS.SI-ID: 1536004292