Classification of perfect and total perfect codes in generalized Petersen graphs

Abstract

In a graph $\hat{I}“$, 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 $\hat{I}“$ such that every vertex of $\hat{I}“$ is adjacent to a unique vertex in $C$. We classify these codes for generalized Petersen graphs.