The status of a vertex v in a connected graph is the sum of the distances from v to all other vertices. The status sequence of a connected graph is the list of the statuses of all the vertices of the graph. In this paper we investigate the status sequences of trees. Particularly, we show that it is NP-complete to decide whether there exists a tree that has a given sequence of integers as its status sequence. We also present some new results about trees whose status sequences are comprised of a few distinct numbers or many distinct numbers. In this direction, we show that any status injective tree is unique among trees. Finally, we investigate how orbit partitions and equitable partitions relate to the status sequence.

连接图中顶点v的状态是从v到所有其他顶点的距离之和。连接图的状态序列是图的所有顶点的状态列表。在本文中，我们研究了树木的状态序列。特别地，我们表明确定是否存在以给定的整数序列作为其状态序列的树是NP完全的。我们还提出了一些有关状态树由几个不同的数字或许多不同的数字组成的树的新结果。在这个方向上，我们表明任何状态注入树在树中都是唯一的。最后，我们研究轨道分区和等效分区如何与状态序列相关。