Packing chromatic number of circular fans and mesh of trees

The packing chromatic number $raisebox{2pt}{$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 compute the packing chromatic number for circular fans with two and four chords and mesh of trees.