Classification of perfect and total perfect codes in generalized Petersen graphs

Abstract: In a graph $Γ$, a perfect code is an independent set $C$ with the property that every vertex not in $C$ is adjacent to a unique vertex in $C$, and a total perfect code is a set $C$ of vertices of $Γ$ such that every vertex of $Γ$ is adjacent to a unique vertex in $C$. We classify these codes for generalized Petersen graphs.