On Cayley representations of central Cayley graphs over almost simple groups

Cayley graph over a group G is said to be central if its connection set is a normal subset of G . We prove that every central Cayley graph over a simple group G has at most two pairwise nonequivalent Cayley representations over G associated with the subgroups of Sym (G) induced by left and right multiplications of G . We also provide an algorithm which, given a central Cayley graph Γ over an almost simple group G whose socle is of a bounded index, finds the full set of pairwise nonequivalent Cayley representations of Γ over G in time polynomial in size of G .