The Locating-Chromatic Number of Binary Trees

Let G = ( V , E ) be a connected graph. The locating-chromatic number of G , denoted by χ L ( G ), is the cardinality of a minimum locating coloring of the vertex set V ( G ) such that all vertices have distinct coordinates. The results on locating-chromatic number of graphs are still limited. In particular, the locating-chromatic number of trees is not completely solved. Therefore, in this paper, we study the locating-chromatic number of any binary tree.