Classifying cubic symmetric graphs of order 18p2

A s-arc in a graph is an ordered (s + 1)-tuple (v(0), v(1), center dot center dot center dot, v(s-1), v(s)) of vertices such that v(i-1) is adjacent to v(i) for 1 <= i <= s and v(i-1) not equal v(i+1) for 1 <= i < s. A graph X is called s-regular if its automorphism group acts regularly on the set of its s-arcs. In this paper, we classify all connected cubic s-regular graphs of order 18p(2) for each s >= 1 and each prime p