Perfect Codes in Cayley Sum Graphs

A subset $C$ of the vertex set a graph $\Gamma$ is called perfect code if every at distance no more than one to exactly in $C$. Let $A$ be finite abelian group and $T$ square-free $A$. The Cayley sum with respect connection simple as its set, two vertices $x$ $y$ are adjacent whenever $x+y\in T$. subgroup said some In this paper, we give necessary sufficient conditions for given We also characterize all codes