A new generalization of generalized Petersen graphs

We discuss a new family of cubic graphs, which we call group divisible generalised Petersen graphs (GDGP -graphs), that bears a close resemblance to the family of generalised Petersen graphs, both in definition and properties. The focus of our paper is on determining the algebraic properties of graphs from our new family. We look for highly symmetric graphs, e.g., graphs with large automorphism groups, and vertexor arc-transitive graphs. In particular, we present arithmetic conditions for the defining parameters that guarantee that graphs with these parameters are vertex-transitive or Cayley, and we find one arctransitive GDGP -graph which is neither a CQ graph of Feng and Wang, nor a generalised Petersen graph.