The locating-chromatic number of a graph $G(V,E)$ is 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 not contained in the same partition class. Determining the locating-chromatic number of any tree is a difficult task. In this paper, we propose an algorithm to compute the upper bound on the locating-chromatic number of any tree. To do so, we decompose a tree into caterpillars and then compute the upper bound of the locating-chromatic number of this tree in terms of the ones for these caterpillars.

中文翻译：

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计算树的定位色数的上限

图的色度数 $G（V，Ë）$ 是顶点集的最小解析分区的基数 $V（G）$这样，所有顶点相对于该分区具有不同的坐标，并且每两个相邻的顶点不包含在同一分区类中。确定任何树的定位色数是一项艰巨的任务。在本文中，我们提出了一种算法来计算任何树的定位色数的上限。为此，我们将一棵树分解为毛毛虫，然后根据这些毛毛虫的数量计算该树的定位色数的上限。