Abstract
An automorphism group of a graph is said to be <TEX>$s$</TEX>-regular if it acts regularly on the set of <TEX>$s$</TEX>-arcs in the graph. A graph is <TEX>$s$</TEX>-regular if its full automorphism group is <TEX>$s$</TEX>-regular. In the present paper, all <TEX>$s$</TEX>-regular cubic graphs of order <TEX>$10p^3$</TEX> are classified for each <TEX>$s{\geq}1$</TEX> and each prime <TEX>$p$</TEX>.
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