Regular sets in Cayley graphs

In a graph $$\Gamma $$ with vertex set V, subset C of V is called an (a, b)-regular if every in has exactly neighbors and $$V\setminus C$$ b C, where are nonnegative integers. the literature, (0, 1)-regular sets known as perfect codes (1, total codes. this paper, we prove that, for any finite group G, non-trivial normal subgroup H G code some Cayley then pair integers $$0\leqslant a\leqslant |H|-1$$ b\leqslant |H|$$ such that $$\gcd (2,|H|-1)$$ divides a, also depending on b). A similar result involving proved paper.