A classification of cubic ss-regular graphs of order 16p16p

A graph is ss-regular   if its automorphism group acts regularly on the set of its ss-arcs. In this paper, we classify all cubic ss-regular graphs of order 16p16p for every s≥1s≥1 and every prime pp. As a result, a new infinite family of cubic 1-regular graphs with girth 10 is constructed.