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چکیده
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A perfect code in a graph Γ with vertex set V (Γ) is a subset C of V (Γ) such that every vertex of Γ is at a distance no more than one, to exactly one vertex of C. In other words, every vertex in V (Γ)\C is adjacent to exactly one vertex in C, and no two vertices in C are adjacent. An inverse-closed subset S of a given group G is called a Cayley transversal of a subgroup H in G if S contains exactly one element of each left (right) coset of H. A subgroup H of G is a subgroup perfect code of G, if there exists a Cayley transversal S of H in G containing the identity element, such that H is a perfect code in Cayley graph Cay(G, S). In this paper, we obtain some interesting results for several subgroups of groups such as self normalizing subgroups, Sylow p-subgroups, cyclic and normal subgroups, and subgroup generated by the solutions of the equation of order n; xn = e; of an abelian group, to be a subgroup perfect code of a finite group.
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