Trees with Certain Locating-Chromatic Number
نویسندگان
چکیده
The locating-chromatic number of a graph can be defined as the cardinality of a minimum resolving partition of the vertex set such that all vertices have distinct coordinates with respect to this partition and every two adjacent vertices in are not contained in the same partition class. In this case, the coordinate of a vertex in is expressed in terms of the distances of to all partition classes. This concept is a special case of the graph partition dimension notion. Previous authors have characterized all graphs of order with locatingchromatic number either or 1. They also proved that there exists a tree of order , 5, having locating-chromatic number if and only if ∈ 3,4, ... , 2, . In this paper, we characterize all trees of order with locating-chromatic number , for any integers and , where 3 and 2 .
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