On regular graphs. III

A graph G is locally s-regular if for any two s-arcs of G having the same head there exists a unique automorphism of G mapping the first of these s-arcs to the second. This is a natural generalization of the concept of an s-regular graph. We extend the results of [2] concerning s-regular graphs to this wider class. We also describe an example of a locally 7-regular cubic graph which is not 7-regular.