Packing chromatic number of cycle related graphs

The packing chromatic number $chi_{rho}(G)$ of a graph $G$ is the smallest integer $k$ for which there exists a mapping $pi:V(G)longrightarrow {1,2,...,k}$ such that any two vertices of color $i$ are at distance at least $i+1$. It is a frequency assignment problem used in wireless networks, which is also called Broadcast coloring. It is proved that packing coloring is NP-complete for general graphs and even for trees. In this paper, we give the packing chromatic number for some classes of cycles.