On the strong metric dimension of composed graphs

Marcel Wagner; Yannick Schmitz; Egon Wanke

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arXiv · 2212.04166

On the strong metric dimension of composed graphs

Marcel Wagner·Yannick Schmitz·Egon Wanke

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Abstract

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.

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Marcel Wagner, Yannick Schmitz, Egon Wanke. 2022-12-08. On the strong metric dimension of composed graphs. https://arxiv.org/abs/2212.04166

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