Trees with certain locating-chromatic number

The locating-chromatic number of a graph g can be defined as the cardinality of a minimum resolving partition of the vertex set v(g) such that all vertices have distinct coordinates with respect to this partition and every two adjacent vertices in g are not contained in the same partition class. in this case,the coordinate of a vertex v in g is expressed in terms of the distances of υ to all partition classes. this concept is a special case of the graph partition dimension notion. previous authors have characterized all graphs of order n with locating-chromatic number either n or n − 1. they also proved that there exists a tree of order n,n ≥ 5,having locating-chromatic number k if and only if k ϵ {3,4,…,n − 2,n}. in this paper,we characterize all trees of order n with locating-chromatic number n − t,for any integers n and t,where n > t + 3 and 2 ≤ t