Abstract A set W of vertices of a connected graph G strongly resolves two different vertices x, y ∉ W if either d G (x, W) = d G (x, y) + d G (y, W) or d G (y, W) = d G (y, x) + d G (x, W), where d G (x, W) = min{d(x,w): w ∈ W} and d(x,w) represents the length of a shortest x − w path. An ordered vertex partition Π = {U 1, U 2,…,U k } of a graph G is a strong resolving partition for G, if every two different vertices of G belonging to the same set of the partition are strongly resolved by some other set of Π. The minimum cardinality of any strong resolving partition for G is the strong partition dimension of G. In this article, we obtain several bounds and closed formulae for the strong partition dimension of some families of graphs and give some realization results relating the strong partition dimension, the strong metric dimension and the order of graphs.

中文翻译：

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图的强解析分区的进一步新结果

摘要 如果 d G (x, W) = d G (x, y) + d G (y, W) 或 d G ( y, W) = d G (y, x) + d G (x, W), 其中 d G (x, W) = min{d(x,w): w ∈ W} and d(x,w)表示最短 x - w 路径的长度。图 G 的有序顶点分区 Π = {U 1, U 2,…,U k } 是 G 的强解析分区，如果 G 的属于同一分区集合的每两个不同的顶点被某个分区强解析另一组 Π。G 的任何强分解分区的最小基数是 G 的强分区维数。 在本文中，我们得到了一些图族的强分区维数的几个边界和闭合公式，并给出了一些与强分区维数相关的实现结果，