A bound for the locating chromatic number of trees

Let f be a proper k-coloring of a connected graph G and \Pi=(V_۱,V_۲,\ldots,V_k) be an ordered partition of V(G) into the resulting color classes. For a vertex v of G, the color code of v with respect to \Pi is defined to be the ordered k-tuple c_{{}_\Pi}(v)=(d(v,V_۱),d(v,V_۲),\ldots,d(v,V_k)), where d(v,V_i)=\min\{d(v,x):~x\in V_i\}, ۱\leq i\leq k. If distinct vertices have distinct color codes, then f is called a locating coloring. The minimum number of colors needed in a locating coloring of G is the locating chromatic number of G, denoted by \chi_{L}(G). In this paper, we study the locating chromatic  numbers of trees. We provide a counter example to a theorem of Gary Chartrand et al. [G. Chartrand, D. Erwin, M.A. Henning, P.J. Slater, P. Zhang, The locating-chromatic number of a graph, Bull. Inst. Combin. Appl., ۳۶ (۲۰۰۲) ۸۹-۱۰۱] about the locating chromatic number of trees. Also, we offer a new bound for the locating chromatic number of trees. Then, by constructing a special family of trees, we show that this bound is best possible.