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The metric dimension is quite a well-studied graph parameter. Recently, theadjacency metric dimension and the local metric dimension have been introduced.We combine these variants and introduce the local adjacency metric dimension.We show that the (local) metric dimension of the corona product of a graph oforder $n$ and some non-trivial graph $H$ equals $n$ times the (local) adjacencymetric dimension of $H$. This strong relation also enables us to infercomputational hardness results for computing the (local) metric dimension,based on according hardness results for (local) adjacency metric dimension thatwe also provide. We also study combinatorial properties of the strong productof graphs and emphasize the role different types of twins play in determiningin particular the adjacency metric dimension of a graph.

On the (adjacency) metric dimension of corona and strong product graphs and their local variants: combinatorial and computational results