Classifying cubic $s$-regular graphs of orders $22p $ and $ 22p^{2}$

A graph is $s$-regular if its automorphism group acts regularly on the set of $s$-arcs. In this study, we classify the connected cubic $s$-regular graphs of orders $22p $ and $ 22p^{2}$ for each $ s \geq 1 $, and each prime $p$.