Two vertices $u$ and $v$ of an undirected graph $G$ are strongly resolved by a vertex $w$ if there is a shortest path between $w$ and $u$ containing $v$ or a shortest path between $w$ and $v$ containing $u$. A vertex set $R$ is a strong resolving set for $G$ if for each pair of vertices there is a vertex in $R$ that strongly resolves them. The strong metric dimension of $G$ is the size of a minimum strong resolving set for $G$. We show that a minimum strong resolving set for an undirected graph $G$ can be computed efficiently if and only if a minimum strong resolving set for each biconnected component of $G$ can be computed efficiently.
翻译：如果在美元与美元之间有一条最短的路径,或者在美元与美元之间有一条最短的路径,或者在美元与美元之间有一条最短的路径,则通过一个顶点($)和美元($)来强有力地解决两个顶点($)和美元($),如果每对顶点($)有一个以美元为单位的顶点($),那么顶点($)就为G美元设定的顶点($)就是一个强有力的解决方案。 坚点($)的强点($)是最小的硬点($)的大小($)。 我们表明,只有能够高效地为每个双重部分($)的两重部分($)计算出一个最起码的根点($),才能有效计算出一个最起码的硬点($)。
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