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A total weighting of a graph $G$ is a mapping $\phi$ that assigns a weight toeach vertex and each edge of $G$. The vertex-sum of $v \in V(G)$ with respectto $\phi$ is $S_{\phi}(v)=\sum_{e\in E(v)}\phi(e)+\phi(v)$. A total weightingis proper if adjacent vertices have distinct vertex-sums. A graph $G=(V,E)$ iscalled $(k,k')$-choosable if the following is true: If each vertex $x$ isassigned a set $L(x)$ of $k$ real numbers, and each edge $e$ is assigned a set$L(e)$ of $k'$ real numbers, then there is a proper total weighting $\phi$ with$\phi(y)\in L(y)$ for any $y \in V \cup E$. In this paper, we prove that thegeneralized Petersen graphs are $(1,3)$-choosable.

Generalized Petersen graphs are (1,3)-choosable