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The anti-Ramsey number $Ar(G,H)$ is the maximum number of colors in anedge-coloring of $G$ with no rainbow copy of $H$. In this paper, we determinethe exact anti-Ramsey number in the generalized Petersen graph $P_{n,k}$ forcycles $C_d$, where $1\leq k\leq \lfloor \frac{n-1}{2} \rfloor$ and $5\le d \le6$. We also give an algorithm to obtain the upper bound or lower bound ofanti-Ramsey number.

Anti-Ramsey problems in the generalized Petersen graphs for cycles